Alexandre N Carvalho, José A Langa, James C Robinson
Published 2010-07-26Version 1
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.
The initial value problem for motion of incompressible viscous and heat-conductive fluids in Banach spaces
A quantitative study of radial symmetry for solutions to semilinear equations in $\mathbb{R}^n$
An inverse problem for semilinear equations involving fractional Laplacian
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