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

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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 > 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:	Date Event 2009 Published
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)

Data sourced from Thomson Reuters' Web of Knowledge

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