+publisher:"Brown University" +contributor:("Dafermos, Constantine")

1. Papanicolaou, Andrew L. New Methods in Theory & Applications of Nonlinear Filtering.

Degree: PhD, Applied Mathematics, 2010, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:11376/

► Hidden Markov models are used in countless signal processing problems, and the associated nonlinear filtering algorithms are used to obtain posterior distributions for the hidden… (more)

Subjects/Keywords: filtering

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APA (6^th Edition):

Papanicolaou, A. L. (2010). New Methods in Theory & Applications of Nonlinear Filtering. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:11376/

Chicago Manual of Style (16^th Edition):

Papanicolaou, Andrew L. “New Methods in Theory & Applications of Nonlinear Filtering.” 2010. Doctoral Dissertation, Brown University. Accessed January 16, 2021. https://repository.library.brown.edu/studio/item/bdr:11376/.

MLA Handbook (7^th Edition):

Papanicolaou, Andrew L. “New Methods in Theory & Applications of Nonlinear Filtering.” 2010. Web. 16 Jan 2021.

Vancouver:

Papanicolaou AL. New Methods in Theory & Applications of Nonlinear Filtering. [Internet] [Doctoral dissertation]. Brown University; 2010. [cited 2021 Jan 16]. Available from: https://repository.library.brown.edu/studio/item/bdr:11376/.

Council of Science Editors:

Papanicolaou AL. New Methods in Theory & Applications of Nonlinear Filtering. [Doctoral Dissertation]. Brown University; 2010. Available from: https://repository.library.brown.edu/studio/item/bdr:11376/

2. Zhang, Hong. Regularity Theory of Elliptic and Parabolic Equations and Systems.

Degree: Department of Applied Mathematics, 2017, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:733578/

► In this dissertation, we study regularity theory of elliptic and parabolic equations and systems with irregular coefficients. In the first part of the dissertation, we… (more)

Subjects/Keywords: Applied mathematics

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APA (6^th Edition):

Zhang, H. (2017). Regularity Theory of Elliptic and Parabolic Equations and Systems. (Thesis). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:733578/

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):

Zhang, Hong. “Regularity Theory of Elliptic and Parabolic Equations and Systems.” 2017. Thesis, Brown University. Accessed January 16, 2021. https://repository.library.brown.edu/studio/item/bdr:733578/.

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

MLA Handbook (7^th Edition):

Zhang, Hong. “Regularity Theory of Elliptic and Parabolic Equations and Systems.” 2017. Web. 16 Jan 2021.

Vancouver:

Zhang H. Regularity Theory of Elliptic and Parabolic Equations and Systems. [Internet] [Thesis]. Brown University; 2017. [cited 2021 Jan 16]. Available from: https://repository.library.brown.edu/studio/item/bdr:733578/.

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

Council of Science Editors:

Zhang H. Regularity Theory of Elliptic and Parabolic Equations and Systems. [Thesis]. Brown University; 2017. Available from: https://repository.library.brown.edu/studio/item/bdr:733578/

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

3. 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 January 16, 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. 16 Jan 2021.

Vancouver:

Hadzic M. Stability and instability in the Stefan problem with surface tension. [Internet] [Doctoral dissertation]. Brown University; 2010. [cited 2021 Jan 16]. 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/

4. Ben-Gal, Nitsan. Grow-Up Solutions and Heteroclinics to Infinity for Scalar Parabolic PDEs.

Degree: PhD, Applied Mathematics, 2009, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:245/

► In recent years, there has been a great deal of interest surrounding the study of the asymptotics and global attractor structure for scalar parabolic PDEs… (more)

▼ In recent years, there has been a great deal of interest surrounding the study of the asymptotics and global attractor structure for scalar parabolic PDEs which are either dissipative or undergo finite-time blow-up. This thesis presents solutions to the asymptotics and connection problems for slowly non-dissipative scalar PDEs, i.e. the final remaining class of scalar parabolic reaction-diffusion equations. Such PDEs produce solutions that neither blow up nor are dissipative. These "grow-up" solutions grow to infinite norm in infinite time, and it is the added challenges they introduce that are overcome in this thesis. In the pursuit of this result, a number of new concepts are defined, including slowly non-dissipative PDEs, non-compact global attractors, and the completed inertial manifold. Many of the underlying assumptions used in the study of dissipative PDEs are inapplicable to slowly non-dissipative PDEs. Thus, concepts must be redefined and techniques updated or extended. The effects of a slowly non-dissipative nonlinearity on the global bifurcation diagram are investigated, and the y-map, a technique critical to solving the connection problem for dissipative systems, is extended to slowly non-dissipative PDEs and a wider range of boundary conditions. The completed inertial manifold is introduced and proven to exist for certain classes of slowly non-dissipative equations. The development of this new structure and its advantageous characteristics provide the tools necessary to prove convergence for grow-up solutions which form heteroclinic connections to infinity. The asymptotics of grow-up solutions are determined, and via combining the various expanded techniques, a full decomposition of the non-compact global attractor is produced for a generic choice of nonlinearity. The results are studied for a selection of interesting cases and are shown to hold for both Neumann and Dirichlet boundary conditions. Advisors/Committee Members: Fieldler, Bernold (director), Dafermos, Constantine (reader), Sandstede, Bjorn (reader).

Subjects/Keywords: grow-up

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APA (6^th Edition):

Ben-Gal, N. (2009). Grow-Up Solutions and Heteroclinics to Infinity for Scalar Parabolic PDEs. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:245/

Chicago Manual of Style (16^th Edition):

Ben-Gal, Nitsan. “Grow-Up Solutions and Heteroclinics to Infinity for Scalar Parabolic PDEs.” 2009. Doctoral Dissertation, Brown University. Accessed January 16, 2021. https://repository.library.brown.edu/studio/item/bdr:245/.

MLA Handbook (7^th Edition):

Ben-Gal, Nitsan. “Grow-Up Solutions and Heteroclinics to Infinity for Scalar Parabolic PDEs.” 2009. Web. 16 Jan 2021.

Vancouver:

Ben-Gal N. Grow-Up Solutions and Heteroclinics to Infinity for Scalar Parabolic PDEs. [Internet] [Doctoral dissertation]. Brown University; 2009. [cited 2021 Jan 16]. Available from: https://repository.library.brown.edu/studio/item/bdr:245/.

Council of Science Editors:

Ben-Gal N. Grow-Up Solutions and Heteroclinics to Infinity for Scalar Parabolic PDEs. [Doctoral Dissertation]. Brown University; 2009. Available from: https://repository.library.brown.edu/studio/item/bdr:245/

5. McQuighan, Kelly Teresa. Oscillons Near Hopf Bifurcations of Planar Reaction Diffusion Equations.

Degree: PhD, Applied Mathematics, 2014, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:386200/

► Oscillons are spatially localized, time-periodic structures that have been observed in many natural processes, often under temporally periodic forcing. Near Hopf bifurcations, such systems can… (more)

Subjects/Keywords: dynamical systems

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APA (6^th Edition):

McQuighan, K. T. (2014). Oscillons Near Hopf Bifurcations of Planar Reaction Diffusion Equations. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:386200/

Chicago Manual of Style (16^th Edition):

McQuighan, Kelly Teresa. “Oscillons Near Hopf Bifurcations of Planar Reaction Diffusion Equations.” 2014. Doctoral Dissertation, Brown University. Accessed January 16, 2021. https://repository.library.brown.edu/studio/item/bdr:386200/.

MLA Handbook (7^th Edition):

McQuighan, Kelly Teresa. “Oscillons Near Hopf Bifurcations of Planar Reaction Diffusion Equations.” 2014. Web. 16 Jan 2021.

Vancouver:

McQuighan KT. Oscillons Near Hopf Bifurcations of Planar Reaction Diffusion Equations. [Internet] [Doctoral dissertation]. Brown University; 2014. [cited 2021 Jan 16]. Available from: https://repository.library.brown.edu/studio/item/bdr:386200/.

Council of Science Editors:

McQuighan KT. Oscillons Near Hopf Bifurcations of Planar Reaction Diffusion Equations. [Doctoral Dissertation]. Brown University; 2014. Available from: https://repository.library.brown.edu/studio/item/bdr:386200/

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

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 January 16, 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. 16 Jan 2021.

Vancouver:

Walsh SP. Stratified and steady periodic water waves. [Internet] [Doctoral dissertation]. Brown University; 2010. [cited 2021 Jan 16]. 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/

7. Srinivasan, Ravi. Closure and complete integrability in Burgers turbulence.

Degree: PhD, Applied Mathematics, 2009, Brown University

URL: https://repository.library.brown.edu/studio/item/bdr:158/

► Burgers turbulence (1-D inviscid Burgers equation with random initial data) is a fundamental non-equilibrium model of stochastic coalescence. In this work we demonstrate that at… (more)

Subjects/Keywords: Burgers turbulence

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

APA (6^th Edition):

Srinivasan, R. (2009). Closure and complete integrability in Burgers turbulence. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:158/

Chicago Manual of Style (16^th Edition):

Srinivasan, Ravi. “Closure and complete integrability in Burgers turbulence.” 2009. Doctoral Dissertation, Brown University. Accessed January 16, 2021. https://repository.library.brown.edu/studio/item/bdr:158/.

MLA Handbook (7^th Edition):

Srinivasan, Ravi. “Closure and complete integrability in Burgers turbulence.” 2009. Web. 16 Jan 2021.

Vancouver:

Srinivasan R. Closure and complete integrability in Burgers turbulence. [Internet] [Doctoral dissertation]. Brown University; 2009. [cited 2021 Jan 16]. Available from: https://repository.library.brown.edu/studio/item/bdr:158/.

Council of Science Editors:

Srinivasan R. Closure and complete integrability in Burgers turbulence. [Doctoral Dissertation]. Brown University; 2009. Available from: https://repository.library.brown.edu/studio/item/bdr:158/

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