Characterization of the limit of some higher dimensional thin domain problems
Keywords
Reaction-diffusion equations, thin domainsAbstract
A reaction-diffusion equation on a family of three dimensional thin domains, collapsing onto a two dimensional subspace, is considered. In [< i> The effect of domain squeezing upon the dynamics of reaction-diffusion equations< /i> , J. Differential Equations < b> 173< /b> (2001), 271–320] 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.Downloads
Published
2002-09-01
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1.
ELSKEN, Thomas and PRIZZI, Martino. Characterization of the limit of some higher dimensional thin domain problems. Topological Methods in Nonlinear Analysis. Online. 1 September 2002. Vol. 20, no. 1, pp. 151 - 178. [Accessed 29 March 2024].
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