On curved squeezing and Conley index
Słowa kluczowe
Primary 37B30, 35B25, Secondary 35B40Abstrakt
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}}.Pobrania
Opublikowane
2011-04-23
Jak cytować
1.
RYBAKOWSKI, Krzysztof P. On curved squeezing and Conley index. Topological Methods in Nonlinear Analysis [online]. 23 kwiecień 2011, T. 38, nr 2, s. 207–231. [udostępniono 22.7.2024].
Numer
Dział
Articles
Statystyki
Liczba wyświetleń i pobrań: 0
Liczba cytowań: 0