Finite-dimensional global attractors in Banach spaces
Analysis of PDEs
2010-07-28 v1 Dynamical Systems
Abstract
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.
Cite
@article{arxiv.1007.4567,
title = {Finite-dimensional global attractors in Banach spaces},
author = {Alexandre N Carvalho and José A Langa and James C Robinson},
journal= {arXiv preprint arXiv:1007.4567},
year = {2010}
}