Asymptotic dynamics of reaction-diffusion equations in dumbbell domains

CDSNS Colloquium
Monday, September 14, 2009 - 11:00
1 hour (actually 50 minutes)
Skiles 269
Universidad Complutense de Madrid
We study the behavior of the asymptotic dynamics of a dissipative reaction-diffusion equation in a dumbbell domain, which, roughly speaking, consists of two fixed domains joined by a thin channel. We analyze the behavior of the stationary solutions (solutions of the elliptic problem), their local unstable manifold and the attractor of the equation as the width of the connecting channel goes to zero.