Finite-dimensional global attractors in Banach spaces - Mathematics > Analysis of PDEsReport as inadecuate




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Abstract: We provide bounds on the upper box-counting dimension of negatively invariantsubsets of Banach spaces, a problem that is easily reduced to covering theimage of the unit ball under a linear map by a collection of balls of smallerradius. As an application of the abstract theory we show that the globalattractors of a very broad class of parabolic partial differential equationssemilinear equations in Banach spaces are finite-dimensional.



Author: Alexandre N Carvalho, José A Langa, James C Robinson

Source: https://arxiv.org/







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