Asymptotic dynamics of reaction-diffusion equations in dumbbell domains

Series
CDSNS Colloquium
Time
Monday, September 14, 2009 - 11:00am for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Jose M. Arrieta – Universidad Complutense de Madrid
Organizer
Yingfei Yi
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.