Article
Finite-dimensional global attractors in Banach spaces
Author/s | Carvalho, Alexandre Nolasco
Langa Rosado, José Antonio Robinson, James C. |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2010-12-15 |
Deposit Date | 2016-09-14 |
Published in |
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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 ... 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. |
Project ID. | 302022/2008-2
451761/2008-1 267/2008 2008/53094 2008/55516-3 MTM2008-0088 P07-FQM-02468 FQM314 EP/G007470/1 |
Citation | Carvalho, A.N., Langa Rosado, J.A. y Robinson, J.C. (2010). Finite-dimensional global attractors in Banach spaces. Journal of Differential Equations, 249 (12), 3099-3109. |
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