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You searched for +publisher:"Brown University" +contributor:("Dong, Hongjie"). Showing records 1 – 3 of 3 total matches.

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

Degree: Department of Applied Mathematics, 2017, Brown University

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 consider Schauder and Lp theories for general linear elliptic and parabolic systems with particular types of irregular coefficients. We also establish some new regularity results regarding a model from the fiber reinforced composite material and expand the Lp and Schauder estimates of higher-order parabolic equations and systems to include a large class of irregular coefficients. In the second part of the dissertation, we investigate the regularity problem of nonlinear nonlocal elliptic and parabolic equations. We prove the Schauder estimates for concave fully nonlinear nonlocal parabolic equations and then establish the Dini type estimates for such type of equations. Advisors/Committee Members: Dong, Hongjie (Advisor), Guo, Yan (Reader), Dafermos, Constantine (Reader).

Subjects/Keywords: Applied mathematics

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APA (6th 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 (16th Edition):

Zhang, Hong. “Regularity Theory of Elliptic and Parabolic Equations and Systems.” 2017. Thesis, Brown University. Accessed October 29, 2020. 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 (7th Edition):

Zhang, Hong. “Regularity Theory of Elliptic and Parabolic Equations and Systems.” 2017. Web. 29 Oct 2020.

Vancouver:

Zhang H. Regularity Theory of Elliptic and Parabolic Equations and Systems. [Internet] [Thesis]. Brown University; 2017. [cited 2020 Oct 29]. 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

2. Cai, Yi. Analysis of An Interacting Particle Method for Rare Event Estimation.

Degree: PhD, Applied Mathematics, 2012, Brown University

This thesis is a large deviations study for the performance of an interacting particle method for rare event estimation. The analysis is restricted to a one-dimensional setting, though even in this restricted setting a number of new techniques must be developed. In contrast to the large deviations analysis of related algorithms, for interacting article schemes it is an occupation measure analysis that is relevant, and within this framework many standard assumptions (stationarity, Feller property) can no longer be assumed. The methods developed are not limited to the question of performance analysis, and in fact give the full large deviations principle for such systems. Advisors/Committee Members: Dupuis, Paul (Director), Dong, Hongjie (Reader), Ramanan, Kavita (Reader).

Subjects/Keywords: interacting particle system

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APA (6th Edition):

Cai, Y. (2012). Analysis of An Interacting Particle Method for Rare Event Estimation. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:297522/

Chicago Manual of Style (16th Edition):

Cai, Yi. “Analysis of An Interacting Particle Method for Rare Event Estimation.” 2012. Doctoral Dissertation, Brown University. Accessed October 29, 2020. https://repository.library.brown.edu/studio/item/bdr:297522/.

MLA Handbook (7th Edition):

Cai, Yi. “Analysis of An Interacting Particle Method for Rare Event Estimation.” 2012. Web. 29 Oct 2020.

Vancouver:

Cai Y. Analysis of An Interacting Particle Method for Rare Event Estimation. [Internet] [Doctoral dissertation]. Brown University; 2012. [cited 2020 Oct 29]. Available from: https://repository.library.brown.edu/studio/item/bdr:297522/.

Council of Science Editors:

Cai Y. Analysis of An Interacting Particle Method for Rare Event Estimation. [Doctoral Dissertation]. Brown University; 2012. Available from: https://repository.library.brown.edu/studio/item/bdr:297522/

3. Wu, Lei. From Kinetic Theory to Fluid Mechanics: Viscous Surface Wave and Hydrodynamic Limit.

Degree: PhD, Applied Mathematics, 2015, Brown University

In this dissertation, we mainly discuss two topics of partial differential equations in fluid dynamics and kinetic theory: viscous surface wave and diffusive limit. With respect to viscous surface wave, we consider an incompressible viscous flow without surface tension in a finite-depth domain of three dimensions, with a free top boundary and a fixed bottom boundary. The system is governed by the Navier-Stokes equations in this moving domain and the transport equation on the moving boundary. Following the framework of geometric mapping by Y. Guo and I. Tice, we further prove the local well-posedness with general smooth data and give a simpler proof of global well-posedness. Also, we construct a stable numerical scheme to simulate the evolution of this system by discontinuous Galerkin method. With respect to diffusive limit, we revisit the asymptotic analysis of a steady neutron transport equation in a two-dimensional unit disk with one-speed velocity. We disprove the classical boundary layer theory by a concrete counterexample with a different boundary layer expansion with geometric correction. Also, we provide the correct boundary layer construction with both in-flow and diffusive boundary. Advisors/Committee Members: Guo, Yan (Director), Shu, Chi-Wang (Director), Dong, Hongjie (Reader).

Subjects/Keywords: free surface

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

APA (6th Edition):

Wu, L. (2015). From Kinetic Theory to Fluid Mechanics: Viscous Surface Wave and Hydrodynamic Limit. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:419456/

Chicago Manual of Style (16th Edition):

Wu, Lei. “From Kinetic Theory to Fluid Mechanics: Viscous Surface Wave and Hydrodynamic Limit.” 2015. Doctoral Dissertation, Brown University. Accessed October 29, 2020. https://repository.library.brown.edu/studio/item/bdr:419456/.

MLA Handbook (7th Edition):

Wu, Lei. “From Kinetic Theory to Fluid Mechanics: Viscous Surface Wave and Hydrodynamic Limit.” 2015. Web. 29 Oct 2020.

Vancouver:

Wu L. From Kinetic Theory to Fluid Mechanics: Viscous Surface Wave and Hydrodynamic Limit. [Internet] [Doctoral dissertation]. Brown University; 2015. [cited 2020 Oct 29]. Available from: https://repository.library.brown.edu/studio/item/bdr:419456/.

Council of Science Editors:

Wu L. From Kinetic Theory to Fluid Mechanics: Viscous Surface Wave and Hydrodynamic Limit. [Doctoral Dissertation]. Brown University; 2015. Available from: https://repository.library.brown.edu/studio/item/bdr:419456/

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