Global weak solution of the general Ericksen-Leslie system in dimension two

Speaker: 

Changyou Wang

Institution: 

University of Kentucky

Time: 

Tuesday, May 14, 2013 - 3:00pm to 4:00pm

Host: 

Location: 

306R

 

In this talk, I will discuss the existence of a unique global weak solution
to the general Ericksen-Leslie system in $R^2$, which is smooth away from possiblyfinite many singular times, for any initial data. This is a joint work with Jinrui Huang and Fanghua Lin.

 

Swarm dynamics and equilibria for a nonlocal aggregation model

Speaker: 

Razvan Fetecau

Institution: 

Simon Fraser University

Time: 

Tuesday, March 5, 2013 - 3:00pm

Location: 

RH 306

 

We consider the aggregation equation ρt − ∇ · (ρ∇K ∗ ρ) = 0 in Rn, where the interaction potential K models short-range repulsion and long-range attraction. We study a family of interaction potentials with repulsion given by a Newtonian potential and attraction in the form of a power law. We show global well-posedness of solutions and investigate analytically and numerically the equilibria and their global stability. The equilibria have biologically relevant features, such as finite densities and compact support with sharp boundaries. This is joint work with Yanghong Huang and Theodore Kolokolnikov. 

 

Homogenization of Green and Neumann Functions

Speaker: 

Zhongwei Shen

Institution: 

University of Kentucky

Time: 

Tuesday, March 12, 2013 - 3:00pm to 4:00pm

Host: 

Location: 

306RH

 

In the talk I will describe my recent work, joint with Carlos Kenig and
Fanghua Lin, on homogenization of the Green and Neumann functions for a family of second order elliptic systems with highly oscillatory periodic coefficients. We study the asymptotic behavior of the first derivatives of the Green and Neumann functions, using Dirichlet and Neumann correctors. As a result, we obtain asymptotic expansions of Poisson kernels and the Dirichlet-to-Neumann maps as well as optimal convergence rates in L^p and W^{1,p} for solutions with Dirichlet or Neumann boundary conditions.

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