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Finite-dimensional global attractors in Banach spaces
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Carvalho, Alexandre Nolasco de, Langa, José A. and Robinson, James C. (2010) Finite-dimensional global attractors in Banach spaces. Journal of Differential Equations, Vol.249 (No.12). pp. 3099-3109. doi:10.1016/j.jde.2010.09.032 ISSN 0022-0396.
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Official URL: http://dx.doi.org/10.1016/j.jde.2010.09.032
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. (C) 2010 Elsevier Inc. All rights reserved.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Journal of Differential Equations | ||||
Publisher: | Academic Press | ||||
ISSN: | 0022-0396 | ||||
Official Date: | 15 December 2010 | ||||
Dates: |
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Volume: | Vol.249 | ||||
Number: | No.12 | ||||
Number of Pages: | 11 | ||||
Page Range: | pp. 3099-3109 | ||||
DOI: | 10.1016/j.jde.2010.09.032 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Funder: | CNPq, CAPES/DGU, FAPESP, Brazil, Ministerio de Ciencia e Innovacion, Junta de Andalucia, Engineering and Physical Sciences Research Council (EPSRC) | ||||
Grant number: | 302022/2008-2, 451761/2008-1, 267/2008, 2008/53094, 2008/55516-3, MTM2008-0088, P07-FQM-02468, FQM314, EP/G007470/1 (EPSRC) |
Data sourced from Thomson Reuters' Web of Knowledge
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