On curved squeezing and Conley index
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Primary 37B30, 35B25, Secondary 35B40Abstract
We consider reaction-diffusion equations on a family of domains depending on a parameter $\eps> 0$. As $\eps\to 0$, the domains degenerate to a lower dimensional manifold. Using some abstract results introduced in the recent paper \cite{\rfa{CR2}} we show that there is a limit equation as $\eps\to 0$ and obtain various convergence and admissibility results for the corresponding semiflows. As a consequence, we also establish singular Conley index and homology index continuation results. Under an additional dissipativeness assumption, we also prove existence and upper-semicontinuity of global attractors. The results of this paper extend and refine earlier results of \cite{\rfa{CR1}} and \cite{\rfa{PRR}}.Downloads
Published
2011-04-23
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RYBAKOWSKI, Krzysztof P. On curved squeezing and Conley index. Topological Methods in Nonlinear Analysis. Online. 23 April 2011. Vol. 38, no. 2, pp. 207 - 231. [Accessed 12 December 2024].
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