subject:(Partial Differential Equations )

1. Hadzic, Mahir. Stability and instability in the Stefan problem with surface tension.

Degree: PhD, Applied Mathematics, 2010, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:11068/

► We develop a high-order nonlinear energy method to study the stability of steady states of the Stefan problem with surface tension. There are two prominent… (more)

Subjects/Keywords: partial differential equations

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APA (6^th Edition):

Hadzic, M. (2010). Stability and instability in the Stefan problem with surface tension. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:11068/

Chicago Manual of Style (16^th Edition):

Hadzic, Mahir. “Stability and instability in the Stefan problem with surface tension.” 2010. Doctoral Dissertation, Brown University. Accessed April 10, 2021. https://repository.library.brown.edu/studio/item/bdr:11068/.

MLA Handbook (7^th Edition):

Hadzic, Mahir. “Stability and instability in the Stefan problem with surface tension.” 2010. Web. 10 Apr 2021.

Vancouver:

Hadzic M. Stability and instability in the Stefan problem with surface tension. [Internet] [Doctoral dissertation]. Brown University; 2010. [cited 2021 Apr 10]. Available from: https://repository.library.brown.edu/studio/item/bdr:11068/.

Council of Science Editors:

Hadzic M. Stability and instability in the Stefan problem with surface tension. [Doctoral Dissertation]. Brown University; 2010. Available from: https://repository.library.brown.edu/studio/item/bdr:11068/

2. Iyer, Sameer S. Boundary Layers for 2D Stationary Navier-Stokes Flows over a Moving Boundary.

Degree: Department of Applied Mathematics, 2018, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:792680/

► In this thesis, we study Prandtl's boundary layer theory for 2D, stationary, incompressible Navier-Stokes flows posed on domains with boundaries. The boundary layer hypothesis posed… (more)

Subjects/Keywords: Differential equations; Partial

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APA (6^th Edition):

Iyer, S. S. (2018). Boundary Layers for 2D Stationary Navier-Stokes Flows over a Moving Boundary. (Thesis). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:792680/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Iyer, Sameer S. “Boundary Layers for 2D Stationary Navier-Stokes Flows over a Moving Boundary.” 2018. Thesis, Brown University. Accessed April 10, 2021. https://repository.library.brown.edu/studio/item/bdr:792680/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Iyer, Sameer S. “Boundary Layers for 2D Stationary Navier-Stokes Flows over a Moving Boundary.” 2018. Web. 10 Apr 2021.

Vancouver:

Iyer SS. Boundary Layers for 2D Stationary Navier-Stokes Flows over a Moving Boundary. [Internet] [Thesis]. Brown University; 2018. [cited 2021 Apr 10]. Available from: https://repository.library.brown.edu/studio/item/bdr:792680/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Iyer SS. Boundary Layers for 2D Stationary Navier-Stokes Flows over a Moving Boundary. [Thesis]. Brown University; 2018. Available from: https://repository.library.brown.edu/studio/item/bdr:792680/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

3. Walsh, Samuel Peter. Stratified and steady periodic water waves.

Degree: PhD, Applied Mathematics, 2010, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:11084/

► This thesis considers two-dimensional stratified water waves propagating under the force of gravity over an impermeable flat bed and with a free surface. In the… (more)

Subjects/Keywords: partial differential equations

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APA (6^th Edition):

Walsh, S. P. (2010). Stratified and steady periodic water waves. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:11084/

Chicago Manual of Style (16^th Edition):

Walsh, Samuel Peter. “Stratified and steady periodic water waves.” 2010. Doctoral Dissertation, Brown University. Accessed April 10, 2021. https://repository.library.brown.edu/studio/item/bdr:11084/.

MLA Handbook (7^th Edition):

Walsh, Samuel Peter. “Stratified and steady periodic water waves.” 2010. Web. 10 Apr 2021.

Vancouver:

Walsh SP. Stratified and steady periodic water waves. [Internet] [Doctoral dissertation]. Brown University; 2010. [cited 2021 Apr 10]. Available from: https://repository.library.brown.edu/studio/item/bdr:11084/.

Council of Science Editors:

Walsh SP. Stratified and steady periodic water waves. [Doctoral Dissertation]. Brown University; 2010. Available from: https://repository.library.brown.edu/studio/item/bdr:11084/

4. Malik, Numann. Dark soliton linearization of the 1D Gross-Pitaevskii equation.

Degree: Department of Mathematics, 2018, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:792705/

► We study the one-dimensional Gross-Pitaevskii equation, a cubic defocusing non-linear Schrodinger equation with nonvanishing boundary conditions. In particular we linearize around the dark solitons, which… (more)

Subjects/Keywords: Differential equations; Partial

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APA (6^th Edition):

Malik, N. (2018). Dark soliton linearization of the 1D Gross-Pitaevskii equation. (Thesis). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:792705/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Malik, Numann. “Dark soliton linearization of the 1D Gross-Pitaevskii equation.” 2018. Thesis, Brown University. Accessed April 10, 2021. https://repository.library.brown.edu/studio/item/bdr:792705/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Malik, Numann. “Dark soliton linearization of the 1D Gross-Pitaevskii equation.” 2018. Web. 10 Apr 2021.

Vancouver:

Malik N. Dark soliton linearization of the 1D Gross-Pitaevskii equation. [Internet] [Thesis]. Brown University; 2018. [cited 2021 Apr 10]. Available from: https://repository.library.brown.edu/studio/item/bdr:792705/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Malik N. Dark soliton linearization of the 1D Gross-Pitaevskii equation. [Thesis]. Brown University; 2018. Available from: https://repository.library.brown.edu/studio/item/bdr:792705/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Queens University

5. Milne, Tristan. Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation .

Degree: Mathematics and Statistics, 2016, Queens University

URL: http://hdl.handle.net/1974/14738

► We study the Dirichlet to Neumann operator for the Riemannian wave equation on a compact Riemannian manifold. If the Riemannian manifold is modelled as an… (more)

Subjects/Keywords: Partial Differential Equations ; Inverse Problems

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APA (6^th Edition):

Milne, T. (2016). Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation . (Thesis). Queens University. Retrieved from http://hdl.handle.net/1974/14738

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Milne, Tristan. “Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation .” 2016. Thesis, Queens University. Accessed April 10, 2021. http://hdl.handle.net/1974/14738.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Milne, Tristan. “Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation .” 2016. Web. 10 Apr 2021.

Vancouver:

Milne T. Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation . [Internet] [Thesis]. Queens University; 2016. [cited 2021 Apr 10]. Available from: http://hdl.handle.net/1974/14738.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Milne T. Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation . [Thesis]. Queens University; 2016. Available from: http://hdl.handle.net/1974/14738

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of California – Berkeley

6. Brereton, Justin Thomas. A method of constructing invariant measures at fixed mass.

Degree: Mathematics, 2018, University of California – Berkeley

URL: http://www.escholarship.org/uc/item/4f22q7dh

► Invariant measures are a useful tool in constructing and analyzing solutions u(t,x) to nonlinear dispersive partial differential equations, especially when a deterministic well-posedness result is… (more)

Subjects/Keywords: Mathematics; Partial Differential Equations; Probability

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APA (6^th Edition):

Brereton, J. T. (2018). A method of constructing invariant measures at fixed mass. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/4f22q7dh

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Brereton, Justin Thomas. “A method of constructing invariant measures at fixed mass.” 2018. Thesis, University of California – Berkeley. Accessed April 10, 2021. http://www.escholarship.org/uc/item/4f22q7dh.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Brereton, Justin Thomas. “A method of constructing invariant measures at fixed mass.” 2018. Web. 10 Apr 2021.

Vancouver:

Brereton JT. A method of constructing invariant measures at fixed mass. [Internet] [Thesis]. University of California – Berkeley; 2018. [cited 2021 Apr 10]. Available from: http://www.escholarship.org/uc/item/4f22q7dh.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Brereton JT. A method of constructing invariant measures at fixed mass. [Thesis]. University of California – Berkeley; 2018. Available from: http://www.escholarship.org/uc/item/4f22q7dh

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Cambridge

7. Brinkman, Daniel. Modeling and numerics for two partial differential equation systems arising from nanoscale physics.

Degree: PhD, 2013, University of Cambridge

URL: http://www.dspace.cam.ac.uk/handle/1810/244667https://www.repository.cam.ac.uk/bitstream/1810/244667/2/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/244667/3/Brinkman_Thesis.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/244667/4/Brinkman_Thesis.pdf.jpg

► This thesis focuses on the mathematical analysis of two partial differential equation systems. Consistent improvement of mathematical computation allows more and more questions to be… (more)

▼ This thesis focuses on the mathematical analysis of two partial differential equation systems. Consistent improvement of mathematical computation allows more and more questions to be addressed in the form of numerical simulations. At the same time, novel materials arising from advances in physics and material sciences are creating new problems which must be addressed. This thesis is divided into two parts based on analysis of two such materials: organic semiconductors and graphene. In part one we derive a generalized reaction-drift-diffusion model for organic photovoltaic devices – solar cells based on organic semiconductors. After formulating an appropriate self-consistent model (based largely on generalizing partly contradictory previous models), we study the operation of the device in several specific asymptotic regimes. Furthermore, we simulate such devices using a customized 2D hybrid discontinuous Galerkin finite element scheme and compare the numerical results to our asymptotics. Next, we use specialized asymptotic regimes applicable to a broad range of device parameters to justify several assumptions used in the formulation of simplified models which have already been discussed in the literature. We then discuss the potential applicability of the simulations to real devices by discussing which parameters will be the most important for a functioning device. We then give further generic 2D numerical results and discuss the limitations of the model in this regime. Finally, we give several perspectives on proving existence and uniqueness of the model. In part two we derive a second-order finite difference numerical scheme for simulation of the 2D Dirac equation and prove that the method converges in the electromagnetically static case. Of particular interest is the application to electrons in graphene. We demonstrate this convergence numerically with several examples for which explicit solutions are known and discuss the manner in which errors appear and propagate. We furthermore extend the Dirac system with Poisson's equation to investigate interesting electronic effects. In particular, we show that our numerical scheme can successfully simulate a beam-splitter and Veselago lens, both of which have been predicted analytically to appear in graphene.

Subjects/Keywords: Partial differential equations; Photovoltaics; Graphene

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APA (6^th Edition):

Brinkman, D. (2013). Modeling and numerics for two partial differential equation systems arising from nanoscale physics. (Doctoral Dissertation). University of Cambridge. Retrieved from http://www.dspace.cam.ac.uk/handle/1810/244667https://www.repository.cam.ac.uk/bitstream/1810/244667/2/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/244667/3/Brinkman_Thesis.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/244667/4/Brinkman_Thesis.pdf.jpg

Chicago Manual of Style (16^th Edition):

Brinkman, Daniel. “Modeling and numerics for two partial differential equation systems arising from nanoscale physics.” 2013. Doctoral Dissertation, University of Cambridge. Accessed April 10, 2021. http://www.dspace.cam.ac.uk/handle/1810/244667https://www.repository.cam.ac.uk/bitstream/1810/244667/2/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/244667/3/Brinkman_Thesis.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/244667/4/Brinkman_Thesis.pdf.jpg.

MLA Handbook (7^th Edition):

Brinkman, Daniel. “Modeling and numerics for two partial differential equation systems arising from nanoscale physics.” 2013. Web. 10 Apr 2021.

Vancouver:

Brinkman D. Modeling and numerics for two partial differential equation systems arising from nanoscale physics. [Internet] [Doctoral dissertation]. University of Cambridge; 2013. [cited 2021 Apr 10]. Available from: http://www.dspace.cam.ac.uk/handle/1810/244667https://www.repository.cam.ac.uk/bitstream/1810/244667/2/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/244667/3/Brinkman_Thesis.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/244667/4/Brinkman_Thesis.pdf.jpg.

Council of Science Editors:

Brinkman D. Modeling and numerics for two partial differential equation systems arising from nanoscale physics. [Doctoral Dissertation]. University of Cambridge; 2013. Available from: http://www.dspace.cam.ac.uk/handle/1810/244667https://www.repository.cam.ac.uk/bitstream/1810/244667/2/license.txt ; https://www.repository.cam.ac.uk/bitstream/1810/244667/3/Brinkman_Thesis.pdf.txt ; https://www.repository.cam.ac.uk/bitstream/1810/244667/4/Brinkman_Thesis.pdf.jpg

University of Colorado

8. Maiden, Michelle. Dispersive hydrodynamics in viscous fluid conduits.

Degree: PhD, Applied Mathematics, 2019, University of Colorado

URL: https://scholar.colorado.edu/appm_gradetds/141

► Viscous fluid conduits provide an ideal system for the study of dissipationless, dispersive hydrodynamics. A dense, viscous fluid serves as the background medium through… (more)

Subjects/Keywords: Fluid Dynamics; Partial Differential Equations

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APA (6^th Edition):

Maiden, M. (2019). Dispersive hydrodynamics in viscous fluid conduits. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/141

Chicago Manual of Style (16^th Edition):

Maiden, Michelle. “Dispersive hydrodynamics in viscous fluid conduits.” 2019. Doctoral Dissertation, University of Colorado. Accessed April 10, 2021. https://scholar.colorado.edu/appm_gradetds/141.

MLA Handbook (7^th Edition):

Maiden, Michelle. “Dispersive hydrodynamics in viscous fluid conduits.” 2019. Web. 10 Apr 2021.

Vancouver:

Maiden M. Dispersive hydrodynamics in viscous fluid conduits. [Internet] [Doctoral dissertation]. University of Colorado; 2019. [cited 2021 Apr 10]. Available from: https://scholar.colorado.edu/appm_gradetds/141.

Council of Science Editors:

Maiden M. Dispersive hydrodynamics in viscous fluid conduits. [Doctoral Dissertation]. University of Colorado; 2019. Available from: https://scholar.colorado.edu/appm_gradetds/141

Rice University

9. Do, Tam. Global Regularity and Finite-time Blow-up in Model Fluid Equations.

Degree: PhD, Natural Sciences, 2017, Rice University

URL: http://hdl.handle.net/1911/96084

► Determining the long time behavior of many partial differential equations modeling fluids has been a challenge for many years. In particular, for many of these… (more)

▼ Determining the long time behavior of many partial differential equations modeling fluids has been a challenge for many years. In particular, for many of these equations, the question of whether solutions exist for all time or form singularities is still open. The structure of the nonlinearity and non-locality in these equations makes their analysis difficult using classical methods. In recent years, many models have been proposed to study fluid equations. In this thesis, we will review some new result in regards to these models as well as give insight into the relation between these models and the true equations. First, we analyze a one-dimensional model for the two-dimensional surface quasi-geostrophic equation and vortex sheets. The model gained prominence due to the work of Cordoba, Cordoba, and Fontelos and is often referred to as the CCF model. We will show that solutions are globally regular in the presence of logarithmically supercritcal dissipation and that solutions eventually gain regularity in the presence of supercritical dissipation. Finally, by analyzing a dyadic model of the equation, we will gain insight into how certain possible singularities in the CCF model can be supressed by dissipation. For the second part of this thesis, we study some one-dimensional model equations for the Euler equations. These models are influenced by the recent numerical simulations of Tom Hou and Guo Luo. They observed possible singularity formation for the three-dimensional Euler equation at the boundary of a cylindrical domain under certain symmetry assumptions. Under these assumptions, a singularity was observed numerically and the solution was observe to have hyperbolic structure near the singularity. Hou and Luo proposed a one-dimensional model system to study singularity formation theoritically. We will study a family of one-dimensional models generalizing their model. The results in chapter 2 are the results of joint work with A. Kiselev, V. Hoang, M. Radosz, and X. Xu. Advisors/Committee Members: Kiselev, Alexander (advisor).

Subjects/Keywords: fluid mechanics; partial differential equations

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APA (6^th Edition):

Do, T. (2017). Global Regularity and Finite-time Blow-up in Model Fluid Equations. (Doctoral Dissertation). Rice University. Retrieved from http://hdl.handle.net/1911/96084

Chicago Manual of Style (16^th Edition):

Do, Tam. “Global Regularity and Finite-time Blow-up in Model Fluid Equations.” 2017. Doctoral Dissertation, Rice University. Accessed April 10, 2021. http://hdl.handle.net/1911/96084.

MLA Handbook (7^th Edition):

Do, Tam. “Global Regularity and Finite-time Blow-up in Model Fluid Equations.” 2017. Web. 10 Apr 2021.

Vancouver:

Do T. Global Regularity and Finite-time Blow-up in Model Fluid Equations. [Internet] [Doctoral dissertation]. Rice University; 2017. [cited 2021 Apr 10]. Available from: http://hdl.handle.net/1911/96084.

Council of Science Editors:

Do T. Global Regularity and Finite-time Blow-up in Model Fluid Equations. [Doctoral Dissertation]. Rice University; 2017. Available from: http://hdl.handle.net/1911/96084

Princeton University

10. Hernandez, Matthew. Mechanisms of Lagrangian Analyticity in Fluids .

Degree: PhD, 2017, Princeton University

URL: http://arks.princeton.edu/ark:/88435/dsp01x346d677z

► Certain systems of inviscid fluid dynamics have the property that for solutions with just a modest amount of regularity in Eulerian variables, the corresponding Lagrangian… (more)

Subjects/Keywords: analysis; partial differential equations

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APA (6^th Edition):

Hernandez, M. (2017). Mechanisms of Lagrangian Analyticity in Fluids . (Doctoral Dissertation). Princeton University. Retrieved from http://arks.princeton.edu/ark:/88435/dsp01x346d677z

Chicago Manual of Style (16^th Edition):

Hernandez, Matthew. “Mechanisms of Lagrangian Analyticity in Fluids .” 2017. Doctoral Dissertation, Princeton University. Accessed April 10, 2021. http://arks.princeton.edu/ark:/88435/dsp01x346d677z.

MLA Handbook (7^th Edition):

Hernandez, Matthew. “Mechanisms of Lagrangian Analyticity in Fluids .” 2017. Web. 10 Apr 2021.

Vancouver:

Hernandez M. Mechanisms of Lagrangian Analyticity in Fluids . [Internet] [Doctoral dissertation]. Princeton University; 2017. [cited 2021 Apr 10]. Available from: http://arks.princeton.edu/ark:/88435/dsp01x346d677z.

Council of Science Editors:

Hernandez M. Mechanisms of Lagrangian Analyticity in Fluids . [Doctoral Dissertation]. Princeton University; 2017. Available from: http://arks.princeton.edu/ark:/88435/dsp01x346d677z

University of Waterloo

11. Murley, Jonathan. The two-space homogenization method.

Degree: 2012, University of Waterloo

URL: http://hdl.handle.net/10012/7099

► In this thesis, we consider the two-space homogenization method, which produces macroscopic expressions out of descriptions of the behaviour of the microstructure. Specifically, we focus… (more)

Subjects/Keywords: homogenization; poroelasticity; partial differential equations

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APA (6^th Edition):

Murley, J. (2012). The two-space homogenization method. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/7099

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Murley, Jonathan. “The two-space homogenization method.” 2012. Thesis, University of Waterloo. Accessed April 10, 2021. http://hdl.handle.net/10012/7099.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Murley, Jonathan. “The two-space homogenization method.” 2012. Web. 10 Apr 2021.

Vancouver:

Murley J. The two-space homogenization method. [Internet] [Thesis]. University of Waterloo; 2012. [cited 2021 Apr 10]. Available from: http://hdl.handle.net/10012/7099.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Murley J. The two-space homogenization method. [Thesis]. University of Waterloo; 2012. Available from: http://hdl.handle.net/10012/7099

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Kansas

12. Lewis, Peter. Regularity of Stochastic Burgers’-Type Equations.

Degree: PhD, Mathematics, 2018, University of Kansas

URL: http://hdl.handle.net/1808/27802

► In classical partial differential equations (PDEs), it is well known that the solution to Burgers' equation in one spatial dimension with positive viscosity can be… (more)

▼ In classical partial differential equations (PDEs), it is well known that the solution to Burgers' equation in one spatial dimension with positive viscosity can be solved by the so called Hopf-Cole transformation, which linearizes the PDE. In particular, this converts Burgers' equation to the linear heat equation, which can be solved explicitly. On the other hand, the Feynman-Kac formula is a tool that can be used to solve the heat equation probabilistically. An interesting and perhaps surprising result which we prove is that one can still make sense of these approaches to Burgers' equation in the presence of space-time white noise, which is very rough. After proving that a suitable Feynman-Kac representation solves stochastic Burgers' equation under a Hopf-Cole transformation, we study some regularity properties of this solution. In particular, we prove moment estimates and Holder continuity, which can be thought of as how ``big'' the solution gets in time and space, and how ``rough'' this solution can be. From this, we then obtain sub-exponential moments and bounds on the tails of the probability distribution for the solution. Prior to this work, no results about any kinds of moment estimates or tails of distributions for stochastic Burgers'-type equations had been established. Furthermore, only one publication on Burgers' equation contains a discussion of Holder regularity. Given the solution to a stochastic partial differential equation (SPDE), it is natural to ask whether this stochastic process has a well-behaved probability law. For example, does the solution have a smooth probability density function or just an absolutely continuous one? Using some powerful tools from Malliavin calculus, we answer this question for stochastic Burgers' equation with our Hopf-Cole solution. Finally, we study regularity of the probability law of the solution to a more general class of semilinear SPDEs which contain Burgers' equation as an example. These results take a less tangible approach since there is no explicit representation for solutions to these equations. However, as we will see, there are some clever techniques and interesting results that can be used to establish such properties. For example, we prove a comparison theorem for this class of SPDEs which, interestingly enough, will be instrumental in obtaining regularity of the probability density function of the solution at fixed points in time and space. The projects in this thesis are joint work of the author and David Nualart. Advisors/Committee Members: Nualart, David (advisor), Alexander, Perry (cmtemember), Feng, Jin (cmtemember), Johnson, Mat (cmtemember), Soo, Terry (cmtemember).

Subjects/Keywords: Mathematics; Stochastic partial differential equations

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APA (6^th Edition):

Lewis, P. (2018). Regularity of Stochastic Burgers’-Type Equations. (Doctoral Dissertation). University of Kansas. Retrieved from http://hdl.handle.net/1808/27802

Chicago Manual of Style (16^th Edition):

Lewis, Peter. “Regularity of Stochastic Burgers’-Type Equations.” 2018. Doctoral Dissertation, University of Kansas. Accessed April 10, 2021. http://hdl.handle.net/1808/27802.

MLA Handbook (7^th Edition):

Lewis, Peter. “Regularity of Stochastic Burgers’-Type Equations.” 2018. Web. 10 Apr 2021.

Vancouver:

Lewis P. Regularity of Stochastic Burgers’-Type Equations. [Internet] [Doctoral dissertation]. University of Kansas; 2018. [cited 2021 Apr 10]. Available from: http://hdl.handle.net/1808/27802.

Council of Science Editors:

Lewis P. Regularity of Stochastic Burgers’-Type Equations. [Doctoral Dissertation]. University of Kansas; 2018. Available from: http://hdl.handle.net/1808/27802

University of Texas – Austin

13. -5659-3170. Pinched manifolds becoming dull.

Degree: PhD, Mathematics, 2018, University of Texas – Austin

URL: http://hdl.handle.net/2152/67650

► In this thesis, we prove short-time existence for Ricci flow, for a class of metrics with unbounded curvature. Our primary motivation in investigating this class… (more)

Subjects/Keywords: Ricci flow; Partial differential equations

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APA (6^th Edition):

-5659-3170. (2018). Pinched manifolds becoming dull. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/67650

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Chicago Manual of Style (16^th Edition):

-5659-3170. “Pinched manifolds becoming dull.” 2018. Doctoral Dissertation, University of Texas – Austin. Accessed April 10, 2021. http://hdl.handle.net/2152/67650.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

MLA Handbook (7^th Edition):

-5659-3170. “Pinched manifolds becoming dull.” 2018. Web. 10 Apr 2021.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

-5659-3170. Pinched manifolds becoming dull. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2018. [cited 2021 Apr 10]. Available from: http://hdl.handle.net/2152/67650.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Council of Science Editors:

-5659-3170. Pinched manifolds becoming dull. [Doctoral Dissertation]. University of Texas – Austin; 2018. Available from: http://hdl.handle.net/2152/67650

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Michigan State University

14. Wei, Yan. Direct analysis of implied volatility for European options.

Degree: 2012, Michigan State University

URL: http://etd.lib.msu.edu/islandora/object/etd:1335

►

Thesis Ph. D. Michigan State University. Applied Mathematics 2012.

We show existence and uniqueness of a strong solution to a linear non-uniformly parabolic equation, which… (more)

Subjects/Keywords: Differential equations, Partial; Applied mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Wei, Y. (2012). Direct analysis of implied volatility for European options. (Thesis). Michigan State University. Retrieved from http://etd.lib.msu.edu/islandora/object/etd:1335

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Wei, Yan. “Direct analysis of implied volatility for European options.” 2012. Thesis, Michigan State University. Accessed April 10, 2021. http://etd.lib.msu.edu/islandora/object/etd:1335.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Wei, Yan. “Direct analysis of implied volatility for European options.” 2012. Web. 10 Apr 2021.

Vancouver:

Wei Y. Direct analysis of implied volatility for European options. [Internet] [Thesis]. Michigan State University; 2012. [cited 2021 Apr 10]. Available from: http://etd.lib.msu.edu/islandora/object/etd:1335.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Wei Y. Direct analysis of implied volatility for European options. [Thesis]. Michigan State University; 2012. Available from: http://etd.lib.msu.edu/islandora/object/etd:1335

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Oxford

15. Gazca Orozco, Pablo Alexei. Numerical analysis of implicitly constituted incompressible fluids : mixed formulations.

Degree: PhD, 2020, University of Oxford

URL: http://ora.ox.ac.uk/objects/uuid:adcdd7ab-1cac-4a3a-bb8c-eada86d7808d ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.820730

► We consider the numerical approximation of incompressible non-Newtonian flow by means of the finite element method, where the constitutive law is defined through an implicit… (more)

▼ We consider the numerical approximation of incompressible non-Newtonian flow by means of the finite element method, where the constitutive law is defined through an implicit relation G(S ,D(u)) = 0. The setting considered in this work captures models widely used in applications, such as the Bingham and the Carreau–Yasuda constitutive relations. Since in general it is not possible to solve for the shear stress S in the constitutive relation, the emphasis is placed on formulations treating the shear stress as a variable. Under the assumption that the constitutive relation defines a monotone graph with r-growth, and that the finite element spaces satisfy appropriate inf-sup stability conditions, the first part of the thesis extends earlier results in the literature to provide a convergence result that guarantees that a subsequence of the numerical approximations converges weakly to a solution of the system, in the optimal range r > 2d/(d+2), where d is the spatial dimension. The qualitative nature of this convergence result is a consequence of the generality of the framework of implicitly constituted fluids, for which e.g. higher regularity estimates are not available. Computational examples show, nevertheless, that the numerical scheme considered exhibits the expected convergence rates, in the situations where these are available. In the second part of the thesis we develop an augmented Lagrangian preconditioner for a stress-velocity-pressure formulation of the steady system. The preconditioner involves a specialised multigrid algorithm that makes use of a space decomposition that captures the kernel of the divergence operator, and non-standard intergrid transfer operators. Although the current theory for robust multigrid works only for symmetric and positive-definite systems (and thus does not apply to the systems considered in this thesis), the resulting preconditioner exhibits remarkable robustness properties. In the final chapter of the thesis, the extension to the anisothermal case is carried out. We employ an implicit constitutive relation that allows for a temperature dependence of rheological parameters such as the viscosity and the yield stress, and provide convergence results for the unsteady forced convection system that takes the viscous dissipation term S : D (u) into account, and for the steady Oberbeck–Boussinesq approximation. For the latter an augmented Lagrangian preconditioner is also introduced; this preconditioner exhibits robust convergence behaviour when applied to the Navier–Stokes and power-law systems, including temperature-dependent viscosity, heat conductivity, and viscous dissipation.

Subjects/Keywords: Numerical Analysis; Partial Differential Equations

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APA (6^th Edition):

Gazca Orozco, P. A. (2020). Numerical analysis of implicitly constituted incompressible fluids : mixed formulations. (Doctoral Dissertation). University of Oxford. Retrieved from http://ora.ox.ac.uk/objects/uuid:adcdd7ab-1cac-4a3a-bb8c-eada86d7808d ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.820730

Chicago Manual of Style (16^th Edition):

Gazca Orozco, Pablo Alexei. “Numerical analysis of implicitly constituted incompressible fluids : mixed formulations.” 2020. Doctoral Dissertation, University of Oxford. Accessed April 10, 2021. http://ora.ox.ac.uk/objects/uuid:adcdd7ab-1cac-4a3a-bb8c-eada86d7808d ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.820730.

MLA Handbook (7^th Edition):

Gazca Orozco, Pablo Alexei. “Numerical analysis of implicitly constituted incompressible fluids : mixed formulations.” 2020. Web. 10 Apr 2021.

Vancouver:

Gazca Orozco PA. Numerical analysis of implicitly constituted incompressible fluids : mixed formulations. [Internet] [Doctoral dissertation]. University of Oxford; 2020. [cited 2021 Apr 10]. Available from: http://ora.ox.ac.uk/objects/uuid:adcdd7ab-1cac-4a3a-bb8c-eada86d7808d ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.820730.

Council of Science Editors:

Gazca Orozco PA. Numerical analysis of implicitly constituted incompressible fluids : mixed formulations. [Doctoral Dissertation]. University of Oxford; 2020. Available from: http://ora.ox.ac.uk/objects/uuid:adcdd7ab-1cac-4a3a-bb8c-eada86d7808d ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.820730

University of Louisville

16. Paniagua Mejia, Carlos M. Mathematical hybrid models for image segmentation.

Degree: PhD, 2016, University of Louisville

URL: 10.18297/etd/2534 ; https://ir.library.louisville.edu/etd/2534

► Two hybrid image segmentation models that are able to process a wide variety of images are proposed. The models take advantage of global (region)… (more)

Subjects/Keywords: partial; differential; equations; image; segmentation; Other Applied Mathematics; Partial Differential Equations

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APA (6^th Edition):

Paniagua Mejia, C. M. (2016). Mathematical hybrid models for image segmentation. (Doctoral Dissertation). University of Louisville. Retrieved from 10.18297/etd/2534 ; https://ir.library.louisville.edu/etd/2534

Chicago Manual of Style (16^th Edition):

Paniagua Mejia, Carlos M. “Mathematical hybrid models for image segmentation.” 2016. Doctoral Dissertation, University of Louisville. Accessed April 10, 2021. 10.18297/etd/2534 ; https://ir.library.louisville.edu/etd/2534.

MLA Handbook (7^th Edition):

Paniagua Mejia, Carlos M. “Mathematical hybrid models for image segmentation.” 2016. Web. 10 Apr 2021.

Vancouver:

Paniagua Mejia CM. Mathematical hybrid models for image segmentation. [Internet] [Doctoral dissertation]. University of Louisville; 2016. [cited 2021 Apr 10]. Available from: 10.18297/etd/2534 ; https://ir.library.louisville.edu/etd/2534.

Council of Science Editors:

Paniagua Mejia CM. Mathematical hybrid models for image segmentation. [Doctoral Dissertation]. University of Louisville; 2016. Available from: 10.18297/etd/2534 ; https://ir.library.louisville.edu/etd/2534

University of Oxford

17. Lee, Hwasung. Strominger's system on non-Kähler hermitian manifolds.

Degree: PhD, 2011, University of Oxford

URL: http://ora.ox.ac.uk/objects/uuid:d3956c4f-c262-4bbf-8451-8dac35f6abef ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.572657

► In this thesis, we investigate the Strominger system on non-Kähler manifolds. We will present a natural generalization of the Strominger system for non-Kähler hermitian manifolds… (more)

Subjects/Keywords: 516.07; Partial differential equations; Differential geometry

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APA (6^th Edition):

Lee, H. (2011). Strominger's system on non-Kähler hermitian manifolds. (Doctoral Dissertation). University of Oxford. Retrieved from http://ora.ox.ac.uk/objects/uuid:d3956c4f-c262-4bbf-8451-8dac35f6abef ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.572657

Chicago Manual of Style (16^th Edition):

Lee, Hwasung. “Strominger's system on non-Kähler hermitian manifolds.” 2011. Doctoral Dissertation, University of Oxford. Accessed April 10, 2021. http://ora.ox.ac.uk/objects/uuid:d3956c4f-c262-4bbf-8451-8dac35f6abef ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.572657.

MLA Handbook (7^th Edition):

Lee, Hwasung. “Strominger's system on non-Kähler hermitian manifolds.” 2011. Web. 10 Apr 2021.

Vancouver:

Lee H. Strominger's system on non-Kähler hermitian manifolds. [Internet] [Doctoral dissertation]. University of Oxford; 2011. [cited 2021 Apr 10]. Available from: http://ora.ox.ac.uk/objects/uuid:d3956c4f-c262-4bbf-8451-8dac35f6abef ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.572657.

Council of Science Editors:

Lee H. Strominger's system on non-Kähler hermitian manifolds. [Doctoral Dissertation]. University of Oxford; 2011. Available from: http://ora.ox.ac.uk/objects/uuid:d3956c4f-c262-4bbf-8451-8dac35f6abef ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.572657

University of Louisville

18. Hapuarachchi, Sujeewa Indika. Regularized solutions for terminal problems of parabolic equations.

Degree: PhD, 2017, University of Louisville

URL: 10.18297/etd/2776 ; https://ir.library.louisville.edu/etd/2776

► The heat equation with a terminal condition problem is not well-posed in the sense of Hadamard so regularization is needed. In general, partial differential… (more)

Subjects/Keywords: partial differential equation; sobolev space; regularization; Partial Differential Equations

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APA (6^th Edition):

Hapuarachchi, S. I. (2017). Regularized solutions for terminal problems of parabolic equations. (Doctoral Dissertation). University of Louisville. Retrieved from 10.18297/etd/2776 ; https://ir.library.louisville.edu/etd/2776

Chicago Manual of Style (16^th Edition):

Hapuarachchi, Sujeewa Indika. “Regularized solutions for terminal problems of parabolic equations.” 2017. Doctoral Dissertation, University of Louisville. Accessed April 10, 2021. 10.18297/etd/2776 ; https://ir.library.louisville.edu/etd/2776.

MLA Handbook (7^th Edition):

Hapuarachchi, Sujeewa Indika. “Regularized solutions for terminal problems of parabolic equations.” 2017. Web. 10 Apr 2021.

Vancouver:

Hapuarachchi SI. Regularized solutions for terminal problems of parabolic equations. [Internet] [Doctoral dissertation]. University of Louisville; 2017. [cited 2021 Apr 10]. Available from: 10.18297/etd/2776 ; https://ir.library.louisville.edu/etd/2776.

Council of Science Editors:

Hapuarachchi SI. Regularized solutions for terminal problems of parabolic equations. [Doctoral Dissertation]. University of Louisville; 2017. Available from: 10.18297/etd/2776 ; https://ir.library.louisville.edu/etd/2776

Rochester Institute of Technology

19. Paulhamus, Marc. Proximal point methods for inverse problems.

Degree: School of Mathematical Sciences (COS), 2011, Rochester Institute of Technology

URL: https://scholarworks.rit.edu/theses/4980

► Numerous mathematical models in applied mathematics can be expressed as a partial differential equation involving certain coefficients. These coefficients are known and they describe some… (more)

▼ Numerous mathematical models in applied mathematics can be expressed as a partial differential equation involving certain coefficients. These coefficients are known and they describe some physical properties of the model. The direct problem in this context is to solve the partial differential equation. By contrast, an inverse problem asks for the identification of the variable coefficients when a certain measurement of a solution of the partial differential equation is available. One of the most commonly used approaches for solving this inverse problem is by posing a constrained minimization problem which can be written as a variational inequality. This paper investigates the inverse problem of identifying certain material parameters in the fourth-order partial differential equations representing the beam and plate models. This inverse problem has attracted a great deal of attention in recent years and has found numerous applications. Since the numerical treatment of the fourth-order problems is rather challenging, the first part of the paper describes in detail the finite element approach for solving the direct problem. The inverse problem is solved by posing an optimization problem whose solution is an approximation of the parameters sought. The optimization problem is solved by gradient based approaches, and in this setting, the most challenging aspect is the computations of the gradient of the objective function. We present a detailed treatment of three approaches to compute the gradient, namely, the so-called adjoint method, adjoint stiffness based approach, and the classical gradient computation. We also present a comparison among these different ways of gradient computation. We use different proximal point methods to solve the inverse problem. It is known that proximal point method is a regularization method which has a significantly different behavior than the well-known Tikhonov regularization method. We present a detailed comparative analysis of the numerical efficiency of several proximal point methods. Advisors/Committee Members: Khan, Akhtar.

Subjects/Keywords: Differential equations; partial; Inverse problems (differential equations) – Numerical solutions

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APA (6^th Edition):

Paulhamus, M. (2011). Proximal point methods for inverse problems. (Thesis). Rochester Institute of Technology. Retrieved from https://scholarworks.rit.edu/theses/4980

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Paulhamus, Marc. “Proximal point methods for inverse problems.” 2011. Thesis, Rochester Institute of Technology. Accessed April 10, 2021. https://scholarworks.rit.edu/theses/4980.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Paulhamus, Marc. “Proximal point methods for inverse problems.” 2011. Web. 10 Apr 2021.

Vancouver:

Paulhamus M. Proximal point methods for inverse problems. [Internet] [Thesis]. Rochester Institute of Technology; 2011. [cited 2021 Apr 10]. Available from: https://scholarworks.rit.edu/theses/4980.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Paulhamus M. Proximal point methods for inverse problems. [Thesis]. Rochester Institute of Technology; 2011. Available from: https://scholarworks.rit.edu/theses/4980

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Columbia University

20. Ghosal, Promit. Time evolution of the Kardar-Parisi-Zhang equation.

Degree: 2020, Columbia University

URL: https://doi.org/10.7916/d8-1xh3-7c82

► The use of the non-linear SPDEs are inevitable in both physics and applied mathematics since many of the physical phenomena in nature can be effectively… (more)

Subjects/Keywords: Mathematics; Statistical mechanics; Stochastic differential equations; Differential equations, Partial; Applied mathematics

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APA (6^th Edition):

Ghosal, P. (2020). Time evolution of the Kardar-Parisi-Zhang equation. (Doctoral Dissertation). Columbia University. Retrieved from https://doi.org/10.7916/d8-1xh3-7c82

Chicago Manual of Style (16^th Edition):

Ghosal, Promit. “Time evolution of the Kardar-Parisi-Zhang equation.” 2020. Doctoral Dissertation, Columbia University. Accessed April 10, 2021. https://doi.org/10.7916/d8-1xh3-7c82.

MLA Handbook (7^th Edition):

Ghosal, Promit. “Time evolution of the Kardar-Parisi-Zhang equation.” 2020. Web. 10 Apr 2021.

Vancouver:

Ghosal P. Time evolution of the Kardar-Parisi-Zhang equation. [Internet] [Doctoral dissertation]. Columbia University; 2020. [cited 2021 Apr 10]. Available from: https://doi.org/10.7916/d8-1xh3-7c82.

Council of Science Editors:

Ghosal P. Time evolution of the Kardar-Parisi-Zhang equation. [Doctoral Dissertation]. Columbia University; 2020. Available from: https://doi.org/10.7916/d8-1xh3-7c82

Loughborough University

21. Yeadon, Cyrus. Approximating solutions of backward doubly stochastic differential equations with measurable coefficients using a time discretization scheme.

Degree: PhD, 2015, Loughborough University

URL: http://hdl.handle.net/2134/20643

► It has been shown that backward doubly stochastic differential equations (BDSDEs) provide a probabilistic representation for a certain class of nonlinear parabolic stochastic partial differential… (more)

▼ It has been shown that backward doubly stochastic differential equations (BDSDEs) provide a probabilistic representation for a certain class of nonlinear parabolic stochastic partial differential equations (SPDEs). It has also been shown that the solution of a BDSDE with Lipschitz coefficients can be approximated by first discretizing time and then calculating a sequence of conditional expectations. Given fixed points in time and space, this approximation has been shown to converge in mean square. In this thesis, we investigate the approximation of solutions of BDSDEs with coefficients that are measurable in time and space using a time discretization scheme with a view towards applications to SPDEs. To achieve this, we require the underlying forward diffusion to have smooth coefficients and we consider convergence in a norm which includes a weighted spatial integral. This combination of smoother forward coefficients and weaker norm allows the use of an equivalence of norms result which is key to our approach. We additionally take a brief look at the approximation of solutions of a class of infinite horizon BDSDEs with a view towards approximating stationary solutions of SPDEs. Whilst we remain agnostic with regards to the implementation of our discretization scheme, our scheme should be amenable to a Monte Carlo simulation based approach. If this is the case, we propose that in addition to being attractive from a performance perspective in higher dimensions, such an approach has a potential advantage when considering measurable coefficients. Specifically, since we only discretize time and effectively rely on simulations of the underlying forward diffusion to explore space, we are potentially less vulnerable to systematically overestimating or underestimating the effects of coefficients with spatial discontinuities than alternative approaches such as finite difference or finite element schemes that do discretize space. Another advantage of the BDSDE approach is that it is possible to derive an upper bound on the error of our method for a fairly broad class of conditions in a single analysis. Furthermore, our conditions seem more general in some respects than is typically considered in the SPDE literature.

Subjects/Keywords: 519.2; Backward doubly stochastic differential equations; Stochastic partial differential equations

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APA (6^th Edition):

Yeadon, C. (2015). Approximating solutions of backward doubly stochastic differential equations with measurable coefficients using a time discretization scheme. (Doctoral Dissertation). Loughborough University. Retrieved from http://hdl.handle.net/2134/20643

Chicago Manual of Style (16^th Edition):

Yeadon, Cyrus. “Approximating solutions of backward doubly stochastic differential equations with measurable coefficients using a time discretization scheme.” 2015. Doctoral Dissertation, Loughborough University. Accessed April 10, 2021. http://hdl.handle.net/2134/20643.

MLA Handbook (7^th Edition):

Yeadon, Cyrus. “Approximating solutions of backward doubly stochastic differential equations with measurable coefficients using a time discretization scheme.” 2015. Web. 10 Apr 2021.

Vancouver:

Yeadon C. Approximating solutions of backward doubly stochastic differential equations with measurable coefficients using a time discretization scheme. [Internet] [Doctoral dissertation]. Loughborough University; 2015. [cited 2021 Apr 10]. Available from: http://hdl.handle.net/2134/20643.

Council of Science Editors:

Yeadon C. Approximating solutions of backward doubly stochastic differential equations with measurable coefficients using a time discretization scheme. [Doctoral Dissertation]. Loughborough University; 2015. Available from: http://hdl.handle.net/2134/20643

Texas Tech University

22. Walker, Billy Kenneth. Estimates on solutions of second order partial differential equations.

Degree: Mathematics, 1974, Texas Tech University

URL: http://hdl.handle.net/2346/10923

Subjects/Keywords: Partial; Differential equations; Differential equations

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Walker, B. K. (1974). Estimates on solutions of second order partial differential equations. (Thesis). Texas Tech University. Retrieved from http://hdl.handle.net/2346/10923

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Walker, Billy Kenneth. “Estimates on solutions of second order partial differential equations.” 1974. Thesis, Texas Tech University. Accessed April 10, 2021. http://hdl.handle.net/2346/10923.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Walker, Billy Kenneth. “Estimates on solutions of second order partial differential equations.” 1974. Web. 10 Apr 2021.

Vancouver:

Walker BK. Estimates on solutions of second order partial differential equations. [Internet] [Thesis]. Texas Tech University; 1974. [cited 2021 Apr 10]. Available from: http://hdl.handle.net/2346/10923.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Walker BK. Estimates on solutions of second order partial differential equations. [Thesis]. Texas Tech University; 1974. Available from: http://hdl.handle.net/2346/10923

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Oregon State University

23. Farlow, Stanley J. Periodic solutions of parabolic partial differential equations.

Degree: PhD, Mathematics, 1967, Oregon State University

URL: http://hdl.handle.net/1957/11824

Subjects/Keywords: Differential equations; Partial

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Farlow, S. J. (1967). Periodic solutions of parabolic partial differential equations. (Doctoral Dissertation). Oregon State University. Retrieved from http://hdl.handle.net/1957/11824

Chicago Manual of Style (16^th Edition):

Farlow, Stanley J. “Periodic solutions of parabolic partial differential equations.” 1967. Doctoral Dissertation, Oregon State University. Accessed April 10, 2021. http://hdl.handle.net/1957/11824.

MLA Handbook (7^th Edition):

Farlow, Stanley J. “Periodic solutions of parabolic partial differential equations.” 1967. Web. 10 Apr 2021.

Vancouver:

Farlow SJ. Periodic solutions of parabolic partial differential equations. [Internet] [Doctoral dissertation]. Oregon State University; 1967. [cited 2021 Apr 10]. Available from: http://hdl.handle.net/1957/11824.

Council of Science Editors:

Farlow SJ. Periodic solutions of parabolic partial differential equations. [Doctoral Dissertation]. Oregon State University; 1967. Available from: http://hdl.handle.net/1957/11824

Oregon State University

24. Kuo, Ying-Ming. Solution of unsteady, two-dimensional, inviscid flows.

Degree: MS, Mechanical Engineering, 1967, Oregon State University

URL: http://hdl.handle.net/1957/47048

► The general theory of characteristics is reviewed for hyperbolic partial differential equations of n independent variables. The application of the theory of characteristics is made… (more)

Subjects/Keywords: Differential equations; Partial

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APA (6^th Edition):

Kuo, Y. (1967). Solution of unsteady, two-dimensional, inviscid flows. (Masters Thesis). Oregon State University. Retrieved from http://hdl.handle.net/1957/47048

Chicago Manual of Style (16^th Edition):

Kuo, Ying-Ming. “Solution of unsteady, two-dimensional, inviscid flows.” 1967. Masters Thesis, Oregon State University. Accessed April 10, 2021. http://hdl.handle.net/1957/47048.

MLA Handbook (7^th Edition):

Kuo, Ying-Ming. “Solution of unsteady, two-dimensional, inviscid flows.” 1967. Web. 10 Apr 2021.

Vancouver:

Kuo Y. Solution of unsteady, two-dimensional, inviscid flows. [Internet] [Masters thesis]. Oregon State University; 1967. [cited 2021 Apr 10]. Available from: http://hdl.handle.net/1957/47048.

Council of Science Editors:

Kuo Y. Solution of unsteady, two-dimensional, inviscid flows. [Masters Thesis]. Oregon State University; 1967. Available from: http://hdl.handle.net/1957/47048

University of Tasmania

25. Wuryatmo, A S(Akhmad Sidik). Approximation solutions of the wave problems.

Degree: 1991, University of Tasmania

URL: https://eprints.utas.edu.au/22335/1/whole_WuryatmoAkhmadSidik1991_thesis.pdf

► In the time dependent situations, the partial differential equations the most closely associated with the wave propagation are of hyperbolic type. Their role in the… (more)

Subjects/Keywords: Differential equations; Partial

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APA (6^th Edition):

Wuryatmo, A. S. S. (1991). Approximation solutions of the wave problems. (Thesis). University of Tasmania. Retrieved from https://eprints.utas.edu.au/22335/1/whole_WuryatmoAkhmadSidik1991_thesis.pdf

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Wuryatmo, A S(Akhmad Sidik). “Approximation solutions of the wave problems.” 1991. Thesis, University of Tasmania. Accessed April 10, 2021. https://eprints.utas.edu.au/22335/1/whole_WuryatmoAkhmadSidik1991_thesis.pdf.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Wuryatmo, A S(Akhmad Sidik). “Approximation solutions of the wave problems.” 1991. Web. 10 Apr 2021.

Vancouver:

Wuryatmo ASS. Approximation solutions of the wave problems. [Internet] [Thesis]. University of Tasmania; 1991. [cited 2021 Apr 10]. Available from: https://eprints.utas.edu.au/22335/1/whole_WuryatmoAkhmadSidik1991_thesis.pdf.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Wuryatmo ASS. Approximation solutions of the wave problems. [Thesis]. University of Tasmania; 1991. Available from: https://eprints.utas.edu.au/22335/1/whole_WuryatmoAkhmadSidik1991_thesis.pdf

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

26. Piriadarshani D. Existence And Computation Of Partial Functional Differential Equations On Unbounded Domains;.

Degree: mathematics, 2013, Anna University

URL: http://shodhganga.inflibnet.ac.in/handle/10603/26436

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This thesis studies numerical approximation of neutral differential newlineequations with infinite delay asymptotic stability of infinite delay differential newlineequations semidiscretization of partial differential equations with… (more)

Subjects/Keywords: Computation; Differential; Equations; Functional; Partial; Unbounded Domains

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

D, P. (2013). Existence And Computation Of Partial Functional Differential Equations On Unbounded Domains;. (Thesis). Anna University. Retrieved from http://shodhganga.inflibnet.ac.in/handle/10603/26436

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

D, Piriadarshani. “Existence And Computation Of Partial Functional Differential Equations On Unbounded Domains;.” 2013. Thesis, Anna University. Accessed April 10, 2021. http://shodhganga.inflibnet.ac.in/handle/10603/26436.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

D, Piriadarshani. “Existence And Computation Of Partial Functional Differential Equations On Unbounded Domains;.” 2013. Web. 10 Apr 2021.

Vancouver:

D P. Existence And Computation Of Partial Functional Differential Equations On Unbounded Domains;. [Internet] [Thesis]. Anna University; 2013. [cited 2021 Apr 10]. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/26436.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

D P. Existence And Computation Of Partial Functional Differential Equations On Unbounded Domains;. [Thesis]. Anna University; 2013. Available from: http://shodhganga.inflibnet.ac.in/handle/10603/26436

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Stellenbosch University

27. Eneyew, Eyaya Birara. Efficient computation of shifted linear systems of equations with application to PDEs.

Degree: MSc, Mathematical Sciences, 2011, Stellenbosch University

URL: http://hdl.handle.net/10019.1/17827

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ENGLISH ABSTRACT: In several numerical approaches to PDEs shifted linear systems of the form (zI - A)x = b, need to be solved for several… (more)

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ENGLISH ABSTRACT: In several numerical approaches to PDEs shifted linear systems of the form (zI - A)x = b, need to be solved for several values of the complex scalar z. Often, these linear systems are large and sparse. This thesis investigates efficient numerical methods for these systems that arise from a contour integral approximation to PDEs and compares these methods with direct solvers. In the first part, we present three model PDEs and discuss numerical approaches to solve them. We use the first problem to demonstrate computations with a dense matrix, the second problem to demonstrate computations with a sparse symmetric matrix and the third problem for a sparse but nonsymmetric matrix. To solve the model PDEs numerically we apply two space discrerization methods, namely the finite difference method and the Chebyshev collocation method. The contour integral method mentioned above is used to integrate with respect to the time variable. In the second part, we study a Hessenberg reduction method for solving shifted linear systems with a dense matrix and present numerical comparison of it with the built-in direct linear system solver in SciPy. Since both are direct methods, in the absence of roundoff errors, they give the same result. However, we find that the Hessenberg reduction method is more efficient in CPU-time than the direct solver. As application we solve a one-dimensional version of the heat equation. In the third part, we present efficient techniques for solving shifted systems with a sparse matrix by Krylov subspace methods. Because of their shift-invariance property, the Krylov methods allow one to obtain approximate solutions for all values of the parameter, by generating a single approximation space. Krylov methods applied to the linear systems are generally slowly convergent and hence preconditioning is necessary to improve the convergence. The use of shift-invert preconditioning is discussed and numerical comparisons with a direct sparse solver are presented. As an application we solve a two-dimensional version of the heat equation with and without a convection term. Our numerical experiments show that the preconditioned Krylov methods are efficient in both computational time and memory space as compared to the direct sparse solver.

AFRIKAANSE OPSOMMING: In verskeie numeriese metodes vir PDVs moet geskuifde lineêre stelsels van die vorm (zI − A)x = b, opgelos word vir verskeie waardes van die komplekse skalaar z. Hierdie stelsels is dikwels groot en yl. Hierdie tesis ondersoek numeriese metodes vir sulke stelsels wat voorkom in kontoerintegraalbenaderings vir PDVs en vergelyk hierdie metodes met direkte metodes vir oplossing. In die eerste gedeelte beskou ons drie model PDVs en bespreek numeriese benaderings om hulle op te los. Die eerste probleem word gebruik om berekenings met ’n vol matriks te demonstreer, die tweede probleem word gebruik om berekenings met yl, simmetriese matrikse te demonstreer en die derde probleem vir yl, onsimmetriese matrikse. Om die …

Advisors/Committee Members: Weideman, J. A. C., Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences..

Subjects/Keywords: Applied mathematics; Partial differential equations; PDEs

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Eneyew, E. B. (2011). Efficient computation of shifted linear systems of equations with application to PDEs. (Masters Thesis). Stellenbosch University. Retrieved from http://hdl.handle.net/10019.1/17827

Chicago Manual of Style (16^th Edition):

Eneyew, Eyaya Birara. “Efficient computation of shifted linear systems of equations with application to PDEs.” 2011. Masters Thesis, Stellenbosch University. Accessed April 10, 2021. http://hdl.handle.net/10019.1/17827.

MLA Handbook (7^th Edition):

Eneyew, Eyaya Birara. “Efficient computation of shifted linear systems of equations with application to PDEs.” 2011. Web. 10 Apr 2021.

Vancouver:

Eneyew EB. Efficient computation of shifted linear systems of equations with application to PDEs. [Internet] [Masters thesis]. Stellenbosch University; 2011. [cited 2021 Apr 10]. Available from: http://hdl.handle.net/10019.1/17827.

Council of Science Editors:

Eneyew EB. Efficient computation of shifted linear systems of equations with application to PDEs. [Masters Thesis]. Stellenbosch University; 2011. Available from: http://hdl.handle.net/10019.1/17827

McMaster University

28. Shimabukuro, Yusuke. Stability and Well-posedness in Integrable Nonlinear Evolution Equations.

Degree: PhD, 2016, McMaster University

URL: http://hdl.handle.net/11375/19500

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This dissertation is concerned with analysis of orbital stability of solitary waves and well-posedness of the Cauchy problem in the integrable evolution equations. The analysis… (more)

Subjects/Keywords: integrable systems; partial differential equations; analysis

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Shimabukuro, Y. (2016). Stability and Well-posedness in Integrable Nonlinear Evolution Equations. (Doctoral Dissertation). McMaster University. Retrieved from http://hdl.handle.net/11375/19500

Chicago Manual of Style (16^th Edition):

Shimabukuro, Yusuke. “Stability and Well-posedness in Integrable Nonlinear Evolution Equations.” 2016. Doctoral Dissertation, McMaster University. Accessed April 10, 2021. http://hdl.handle.net/11375/19500.

MLA Handbook (7^th Edition):

Shimabukuro, Yusuke. “Stability and Well-posedness in Integrable Nonlinear Evolution Equations.” 2016. Web. 10 Apr 2021.

Vancouver:

Shimabukuro Y. Stability and Well-posedness in Integrable Nonlinear Evolution Equations. [Internet] [Doctoral dissertation]. McMaster University; 2016. [cited 2021 Apr 10]. Available from: http://hdl.handle.net/11375/19500.

Council of Science Editors:

Shimabukuro Y. Stability and Well-posedness in Integrable Nonlinear Evolution Equations. [Doctoral Dissertation]. McMaster University; 2016. Available from: http://hdl.handle.net/11375/19500

McMaster University

29. Salmaniw, Yurij. Existence and Regularity of Solutions to Some Singular Parabolic Systems.

Degree: MSc, 2018, McMaster University

URL: http://hdl.handle.net/11375/23982

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This thesis continues the work started with my previous supervisor, Dr. Shaohua Chen. In [15], the authors developed some tools that showed the boundedness or… (more)

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This thesis continues the work started with my previous supervisor, Dr. Shaohua Chen. In [15], the authors developed some tools that showed the boundedness or blowup of solutions to a semilinear parabolic system with homogeneous Neumann boundary conditions. This system, the so called ’Activator-Inhibitor Model’, is of interest as it is used to model biological processes and pattern formation. Similar tools were later adapted to deal with the same parabolic system in [3], in which the authors prove global boundedness of solutions under homogeneous Dirichlet conditions. This new problem is of mathematical interest as the solutions may grow singular near the boundary. Shortly after, a different system was considered in [4], where the authors proved global boundedness of solutions to a system featuring similar singular reaction terms. The goal of this thesis is twofold: first, the tools developed that allow us to tackle these sorts of problems will be demonstrated in detail to showcase its utility; the second is to then use these tools to generalize some of these previous results to a larger class of singular parabolic systems. In doing so, we expand the classical literature found in [14] and other notable works, where nonsingular equations are extensively treated. The motivation for the first should be clear. While there are numerous bodies of text treating nonsingular problems, there are no collections available dealing with these types of singularities exclusively. This is of practical use to other mathematicians studying partial differential equations. The motivation for the second is, perhaps, more practical. There are a growing number of models found in physics, chemistry and biology that may be generalized to a singular type system. Through allowing those individuals to treat these problems, we may gain valuable insights into the real world and how these processes behave.

Thesis

Master of Science (MSc)

Advisors/Committee Members: Bronsard, Lia, Alama, Stanley, Mathematics and Statistics.

Subjects/Keywords: Partial differential equations; Parabolic systems; Singular systems

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Salmaniw, Y. (2018). Existence and Regularity of Solutions to Some Singular Parabolic Systems. (Masters Thesis). McMaster University. Retrieved from http://hdl.handle.net/11375/23982

Chicago Manual of Style (16^th Edition):

Salmaniw, Yurij. “Existence and Regularity of Solutions to Some Singular Parabolic Systems.” 2018. Masters Thesis, McMaster University. Accessed April 10, 2021. http://hdl.handle.net/11375/23982.

MLA Handbook (7^th Edition):

Salmaniw, Yurij. “Existence and Regularity of Solutions to Some Singular Parabolic Systems.” 2018. Web. 10 Apr 2021.

Vancouver:

Salmaniw Y. Existence and Regularity of Solutions to Some Singular Parabolic Systems. [Internet] [Masters thesis]. McMaster University; 2018. [cited 2021 Apr 10]. Available from: http://hdl.handle.net/11375/23982.

Council of Science Editors:

Salmaniw Y. Existence and Regularity of Solutions to Some Singular Parabolic Systems. [Masters Thesis]. McMaster University; 2018. Available from: http://hdl.handle.net/11375/23982

North Carolina State University

30. Taylor, Monique Richardson. Dafermos Regularization of a Modified KdV-Burgers Equation.

Degree: PhD, Applied Mathematics, 2010, North Carolina State University

URL: http://www.lib.ncsu.edu/resolver/1840.16/4034

► This project involves Dafermos regularization of a partial differential equation of order higher than 2. The modified Korteweg de Vries-Burgers equation is u_T + f(u)_X… (more)

Subjects/Keywords: Geometric singular perturbation theory; Partial differential equations

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Taylor, M. R. (2010). Dafermos Regularization of a Modified KdV-Burgers Equation. (Doctoral Dissertation). North Carolina State University. Retrieved from http://www.lib.ncsu.edu/resolver/1840.16/4034

Chicago Manual of Style (16^th Edition):

Taylor, Monique Richardson. “Dafermos Regularization of a Modified KdV-Burgers Equation.” 2010. Doctoral Dissertation, North Carolina State University. Accessed April 10, 2021. http://www.lib.ncsu.edu/resolver/1840.16/4034.

MLA Handbook (7^th Edition):

Taylor, Monique Richardson. “Dafermos Regularization of a Modified KdV-Burgers Equation.” 2010. Web. 10 Apr 2021.

Vancouver:

Taylor MR. Dafermos Regularization of a Modified KdV-Burgers Equation. [Internet] [Doctoral dissertation]. North Carolina State University; 2010. [cited 2021 Apr 10]. Available from: http://www.lib.ncsu.edu/resolver/1840.16/4034.

Council of Science Editors:

Taylor MR. Dafermos Regularization of a Modified KdV-Burgers Equation. [Doctoral Dissertation]. North Carolina State University; 2010. Available from: http://www.lib.ncsu.edu/resolver/1840.16/4034

Open Access Theses and Dissertations