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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. (James Cooper), 1969-.
(2009)
*Lower semicontinuity of attractors for non-autonomous dynamical systems.*
Ergodic Theory and Dynamical Systems, Vol.29
.
pp. 1765-1780.
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 > 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 |

Volume: | Vol.29 |

Page Range: | pp. 1765-1780 |

Identification Number: | 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) |

References: | [1] E. A. M. Abreu and A. N. Carvalho. Lower semicontinuity of attractors for parabolic problems with |

URI: | http://wrap.warwick.ac.uk/id/eprint/3137 |

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