Finite-dimensional global attractors in Banach spaces

Autor(es)

Carvalho, Alexandre N. ^[1] ; Langa, Jose A. ^[2] ; Robinson, James C. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Computacao, BR-13560970 Sao Carlos, SP - Brazil

^[2] Univ Seville, Dept Ecuac Diferenciales & Anal Numer, E-41080 Seville - Spain

^[3] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands - England

• Tipo de documento: Artigo Científico
• Fonte: Journal of Differential Equations; v. 249, n. 12, p. 3099-3109, DEC 15 2010.
• Citações Web of Science: 0

Resumo

We provide bounds on the upper box-counting dimension of negatively invariant subsets of Banach spaces, a problem that is easily reduced to covering the image of the unit ball under a linear map by a collection of balls of smaller radius. As an application of the abstract theory we show that the global attractors of a very broad class of parabolic partial differential equations (semilinear equations in Banach spaces) are finite-dimensional. (C) 2010 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 08/55516-3 - Sistemas dinâmicos não lineares em espaços de dimensão infinita
• Beneficiário: Alexandre Nolasco de Carvalho
• Modalidade de apoio: Auxílio à Pesquisa - Temático