Department of Mathematical Sciences
Carnegie Mellon University

Michel Chipot, University of Zurich

"Asymptotic behaviour for a class of nonlocal problems"

ABSTRACT: We propose new techniques to study the asymptotic behaviour of problems of the type:

$\displaystyle \left\{\begin{array}{rcccl} u_t - a(l(u(t)))\Delta u + u &=& f(x)... ...mathbb{R}^+\\ u(\cdot,0) &=& u_0\quad &\hbox{ in }& \Omega, \end{array}\right.$

(1)

where

$\displaystyle l(u(.,t))= \int_{\Omega} g(x)~u(x,t)dx$

and , $g\in L^2(\Omega)$ , is some continuous function.

In particular we show that finding the associated stationary solutions to (1) reduces to find the solutions of an equation in ${\bf R}$ . Using some Lyapunov functions or some direct methods we are then able to establish various convergence results.

TITLE: ``Asymptotic behaviour for a class of nonlocal problems"

ABSTRACT: We propose new techniques to study the asymptotic behaviour of problems of the type:

$\displaystyle \left\{\begin{array}{rcccl} u_t - a(l(u(t)))\Delta u + u &=& f(x)... ...mathbb{R}^+\\ u(\cdot,0) &=& u_0\quad &\hbox{ in }& \Omega, \end{array}\right.$

(1)

where

$\displaystyle l(u(.,t))= \int_{\Omega} g(x)~u(x,t)dx$

and , $g\in L^2(\Omega)$ , is some continuous function.

Location: PPB 300
Time: 1:30

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