Characterization of the limit of some higher dymensional thin domain problems

Details Characterization of the limit of some higher dymensional thin domain problems Characterization of the limit of some higher dymensional thin domain problems

2002-09-20

arxiv.org/abs/math/0209266v1

Mathematics

Analysis of PDEs

29 pages; 2 figures; to appear in "Topological Methods in Nonlinear Analysis"

Scientific paper

A reaction-diffusion equation on a family of three dimensional thin domains, collapsing onto a two dimensional subspace, is considered. In \cite{\rfa pr..} it was proved that, as the thickness of the domains tends to zero, the solutions of the equations converge in a strong sense to the solutions of an abstract semilinear parabolic equation living in a closed subspace of $H^1$. Also, existence and upper semicontinuity of the attractors was proved. In this work, for a specific class of domains, the limit problem is completely characterized as a system of two-dimensional reaction-diffusion equations, coupled by mean of compatibility and balance boundary conditions.

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