Lower semicontinuity of attractors for non-autonomous dynamical systems


Autoria(s): CARVALHO, Alexandre N.; LANGA, Jose A.; ROBINSON, James C.
Contribuinte(s)

UNIVERSIDADE DE SÃO PAULO

Data(s)

20/10/2012

20/10/2012

2009

Resumo

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.

CNPq[305447/2005-0]

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

CAPES BEX[1353/06-3]

FAPESP, Brazil[03/10042-0]

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Royal Society University Research Fellow

Royal Society University Research Fellow

Identificador

ERGODIC THEORY AND DYNAMICAL SYSTEMS, v.29, p.1765-1780, 2009

0143-3857

http://producao.usp.br/handle/BDPI/28832

10.1017/S0143385708000850

http://dx.doi.org/10.1017/S0143385708000850

Idioma(s)

eng

Publicador

CAMBRIDGE UNIV PRESS

Relação

Ergodic Theory and Dynamical Systems

Direitos

restrictedAccess

Copyright CAMBRIDGE UNIV PRESS

Palavras-Chave #REACTION-DIFFUSION EQUATIONS #DIFFERENTIAL-EQUATIONS #NONHYPERBOLIC ATTRACTOR #ASYMPTOTIC-BEHAVIOR #PARABOLIC PROBLEMS #PERTURBATIONS #CONTINUITY #Mathematics, Applied #Mathematics
Tipo

article

original article

publishedVersion