Finite-dimensional global attractors in Banach spaces

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.

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

CNPq[302022/2008-2]

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

CNPq[451761/2008-1]

CAPES/DGU[267/2008]

DGU

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

FAPESP, Brazil[2008/53094]

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

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

FAPESP, Brazil[2008/55516-3]

Ministerio de Ciencia e Innovacion[MTM2008-0088]

Ministerio de Ciencia e Innovacion

Junta de Andalucia[P07-FQM-02468]

Junta de Andalucia (Spain)

Junta de Andalucia[FQM314]

Junta de Andalucia (Spain)

EPSRC

EPSRC[EP/G007470/1]