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Lower semicontinuity of attractors for non-autonomous dynamical systems

By Alexandre Nolasco de Carvalho, José A. Langa and James C. Robinson


This paper is concerned with the lower semicontinuity of attractors for semilinear\ud non-autonomous differential equations in Banach spaces. We require the unperturbed\ud attractor to be given as the union of unstable manifolds of time-dependent hyperbolic\ud solutions, generalizing previous results valid only for gradient-like systems in which\ud the hyperbolic solutions are equilibria. The tools employed are a study of the continuity\ud of the local unstable manifolds of the hyperbolic solutions and results on the continuity of\ud the exponential dichotomy of the linearization around each of these solutions

Topics: QA
Publisher: Cambridge University Press
Year: 2009
OAI identifier: oai:wrap.warwick.ac.uk:3137

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