Difference between revisions of "PDE Geometric Analysis seminar"

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(Seminar Schedule Spring 2016)
(Seminar Schedule Spring 2016)
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|February 22  
 
|February 22  
 
| Hong Zhang (Brown)
 
| Hong Zhang (Brown)
|[[# Hong Zhang | ]]
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|[[# Hong Zhang | On an elliptic equation arising from composite material ]]
 
| Kim
 
| Kim
 
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Revision as of 06:37, 5 February 2016

The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.

Previous PDE/GA seminars

Tentative schedule for Fall 2016

Seminar Schedule Spring 2016

date speaker title host(s)
January 25 Tianling Jin (HKUST and Caltech) Holder gradient estimates for parabolic homogeneous p-Laplacian equations Zlatos
February 1 Russell Schwab (Michigan State University) Neumann homogenization via integro-differential methods Lin
February 8 Jingrui Cheng (UW Madison) Semi-geostrophic system with variable Coriolis parameter Tran & Kim
February 15 Paul Rabinowitz (UW Madison) Tran & Kim
February 22 Hong Zhang (Brown) On an elliptic equation arising from composite material Kim
February 29 Aaron Yip (Purdue university) TBD Tran
March 7 Hiroyoshi Mitake (Hiroshima university) Selection problem for fully nonlinear equations Tran
March 15 Nestor Guillen (UMass Amherst) TBA Lin
March 21 (Spring Break)
March 28 Ryan Denlinger (Courant Institute) The propagation of chaos for a rarefied gas of hard spheres in vacuum Lee
April 4
April 11
April 18
April 25 Moon-Jin Kang (UT-Austin) Kim
May 2

Abstracts

Tianling Jin

Holder gradient estimates for parabolic homogeneous p-Laplacian equations

We prove interior Holder estimates for the spatial gradient of viscosity solutions to the parabolic homogeneous p-Laplacian equation u_t=|\nabla u|^{2-p} div(|\nabla u|^{p-2}\nabla u), where 1<p<\infty. This equation arises from tug-of-war like stochastic games with white noise. It can also be considered as the parabolic p-Laplacian equation in non divergence form. This is joint work with Luis Silvestre.

Russell Schwab

Neumann homogenization via integro-differential methods

In this talk I will describe how one can use integro-differential methods to attack some Neumann homogenization problems-- that is, describing the effective behavior of solutions to equations with highly oscillatory Neumann data. I will focus on the case of linear periodic equations with a singular drift, which includes (with some regularity assumptions) divergence equations with non-co-normal oscillatory Neumann conditions. The analysis focuses on an induced integro-differential homogenization problem on the boundary of the domain. This is joint work with Nestor Guillen.

Jingrui Cheng

Semi-geostrophic system with variable Coriolis parameter.

The semi-geostrophic system (abbreviated as SG) is a model of large-scale atmospheric/ocean flows. Previous works about the SG system have been restricted to the case of constant Coriolis force, where we write the equation in "dual coordinates" and solve. This method does not apply for variable Coriolis parameter case. We develop a time-stepping procedure to overcome this difficulty and prove local existence and uniqueness of smooth solutions to SG system. This is joint work with Michael Cullen and Mikhail Feldman.

Hiroyoshi Mitake

Selection problem for fully nonlinear equations

Recently, there was substantial progress on the selection problem on the ergodic problem for Hamilton-Jacobi equations, which was open during almost 30 years. In the talk, I will first show a result on the convex Hamilton-Jacobi equation, then tell important problems which still remain. Next, I will mainly focus on a recent joint work with H. Ishii (Waseda U.), and H. V. Tran (U. Wisconsin-Madison) which is about the selection problem for fully nonlinear, degenerate elliptic partial differential equations. I will present a new variational approach for this problem.