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Characterization of the limit of some higher dymensional thin domain problems

T. Elsken, M. Prizzi

math.AParXiv:math/0209266

Abstract

A reaction-diffusion equation on a family of three dimensional thin domains, collapsing onto a two dimensional subspace, is considered. In 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 H1. 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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