Finite-dimensional global attractors in Banach spaces

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:249

Article

Carvalho, Alexandre N.²  Langa, Jose A.³  Robinson, James C.¹ 

[1] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England

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

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

关键词: Global attractors;    Negatively invariant sets;    Box-counting dimension;    Banach-Mazur distance;   

DOI  :  10.1016/j.jde.2010.09.032

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free