Finite-dimensional global attractors in Banach spaces

Details Finite-dimensional global attractors in Banach spaces Finite-dimensional global attractors in Banach spaces

2010-07-26

arxiv.org/abs/1007.4567v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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