Finite-dimensional global attractors in Banach spaces

[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.

[发布日期] 2010-12-15

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