Characterization of the limit of some higher dimensional thin domain problems
KeywordsReaction-diffusion equations, thin domains
AbstractA 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.
How to Cite
ELSKEN, Thomas & PRIZZI, Martino. Characterization of the limit of some higher dimensional thin domain problems. Topological Methods in Nonlinear Analysis [online]. 1 September 2002, T. 20, nr 1, s. 151–178. [accessed 2.2.2023].
Number of views and downloads: 0
Number of citations: 0