On curved squeezing and Conley index

Krzysztof P. Rybakowski

Abstract


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}}.

Keywords


Primary 37B30; 35B25; Secondary 35B40

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