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Characterization of non-autonomous attractors of a perturbed infinite-dimensional gradient system
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Carvalho, Alexandre Nolasco de, Langa, José A., Robinson, James C. and Suarez, Antonio (2007) Characterization of non-autonomous attractors of a perturbed infinite-dimensional gradient system. Journal of Differential Equations, Vol.236 (No.2). pp. 570-603. doi:10.1016/j.jde.2007.01.017 ISSN 0022-0396.
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Official URL: http://dx.doi.org/10.1016/j.jde.2007.01.017
Abstract
In this paper we determine the exact structure of the pullback attractors in non-autonomous problems that are perturbations of autonomous gradient systems with attractors that are the union of the unstable manifolds of a finite set of hyperbolic equilibria. We show that the pullback attractors of the perturbed systems inherit this structure, and are given as the union of the unstable manifolds of a set of hyperbolic global solutions which are the non-autonomous analogues of the hyperbolic equilibria. We also prove, again parallel to the autonomous case, that all solutions converge as t -> + infinity to one of these hyperbolic global solutions. We then show how to apply these results to systems that are asymptotically autonomous as t -> - infinity) and as t -> + infinity, and use these relatively simple test cases to illustrate a discussion of possible definitions of a forwards attractor in the non-autonomous case. (C) 2007 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 May 2007 | ||||
Dates: |
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Volume: | Vol.236 | ||||
Number: | No.2 | ||||
Number of Pages: | 34 | ||||
Page Range: | pp. 570-603 | ||||
DOI: | 10.1016/j.jde.2007.01.017 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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