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Equadiff 2003 - International Conference on Differential Equations
July 22-26, 2003
LUC Diepenbeek
Hasselt, Belgium

Organizers
Freddy Dumortier (Chair, LUC Diepenbeek), Henk Broer (Univ. Groningen), Jean-Pierre Gossez (Univ. Libre Bruxelles), Jean Mawhin (Univ. Cath. Louvain-la-Neuve), Andre Vanderbauwhede (Univ. Gent), Sjoerd Verduyn Lunel (Univ. Leiden)

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Long-time dynamics of reaction-diffusion equations on thin two-layer domains
by
Igor Chueshov
Department of Mechanics and Mathematics, Kharkov University, 4 Svobody sq., 61077, Kharkov, Ukraine
Coauthors: Andrej Rekalo (Kharkov)

We consider a semilinear parabolic equation on a union of thin bounded tube domains \Omega1, \epsilon=\Gamma×(0, \epsilon) and \Omega2, \epsilon=\Gamma×(-\epsilon, 0) joined at the common base (a domain \Gamma subset Rd,  d <= 3). Unknown functions are coupled by some interface boundary condition on \Gamma. This problem can model a reaction-diffusion system of two components reacting at the boundary. The reaction intensity k(x, \epsilon) on the interface depends on \epsilon (i.e. on domain's cross size). We study limiting properties the global attractor of the corresponding evolution semigroup S\epsilon(t) as \epsilon --> 0 (i.e. as the initial domain is getting thinner). These properties depends crucially on the behaviour of the intensity k(x, \epsilon) as \epsilon --> 0 and three completely different scenario are possible.

Date received: May 20, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # calh-54.