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Lower semicontinuity of attractors for non-autonomous dynamical systems
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Carvalho, Alexandre Nolasco de, Langa, José A. and Robinson, James C. (2009) Lower semicontinuity of attractors for non-autonomous dynamical systems. Ergodic Theory and Dynamical Systems, Vol.29 . pp. 1765-1780. doi:10.1017/S0143385708000850 ISSN 0143-3857.
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Official URL: http://dx.doi.org/10.1017/S0143385708000850
Abstract
This paper is concerned with the lower semicontinuity of attractors for semilinear
non-autonomous differential equations in Banach spaces. We require the unperturbed
attractor to be given as the union of unstable manifolds of time-dependent hyperbolic
solutions, generalizing previous results valid only for gradient-like systems in which
the hyperbolic solutions are equilibria. The tools employed are a study of the continuity
of the local unstable manifolds of the hyperbolic solutions and results on the continuity of
the exponential dichotomy of the linearization around each of these solutions.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Banach spaces, Differential equations, Hyperbolic, Attractors (Mathematics), Perturbation (Mathematics) | ||||
| Journal or Publication Title: | Ergodic Theory and Dynamical Systems | ||||
| Publisher: | Cambridge University Press | ||||
| ISSN: | 0143-3857 | ||||
| Official Date: | 2009 | ||||
| Dates: |
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| Volume: | Vol.29 | ||||
| Page Range: | pp. 1765-1780 | ||||
| DOI: | 10.1017/S0143385708000850 | ||||
| Status: | Peer Reviewed | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Funder: | Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil. Coordenação do Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) | ||||
| Grant number: | 305447/2005-0 (CNPq), 1353/06-3 (CAPES BEX), 03/10042-0 (FAPESP) |
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