Dimension of the attractors associated to autonomous and nonautonomous dynamical s...
Continuity of global attractors: Correctors and convergence rates
Estimates of the Fractal Dimension of Attractors for Autonomous and Non-Autonomous...
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| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Sao Paulo, Inst Ciencias Matemat & Computacao, BR-13560970 Sao Carlos, SP - Brazil
[2] Univ Seville, Dept Ecuac Diferenciales & Anal Numer, E-41080 Seville - Spain
[3] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands - England
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | Journal of Differential Equations; v. 249, n. 12, p. 3099-3109, DEC 15 2010. |
| Web of Science Citations: | 0 |
| 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. (AU) | |