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Structure and bifurcation of pullback attractors in a non-autonomous Chafee-Infante equation
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Carvalho, Alexandre Nolasco de, Langa, José A. and Robinson, James C. (2012) Structure and bifurcation of pullback attractors in a non-autonomous Chafee-Infante equation. Proceedings of the American Mathematical Society, Vol.140 (No.7). pp. 2357-2373. doi:10.1090/S0002-9939-2011-11071-2
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Official URL: http://dx.doi.org/10.1090/S0002-9939-2011-11071-2
Abstract
The Chafee-Infante equation is one of the canonical infinite-dimensional dynamical systems for which a complete description of the global attractor is available. In this paper we study the structure of the pullback attractor for a non-autonomous version of this equation, ut = uxx + λu - β(t)u3, and investigate the bifurcations that this attractor undergoes as λ is varied. We are able to describe these in some detail, despite the fact that our model is truly non-autonomous; i.e., we do not restrict to 'small perturbations' of the autonomous case.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science > Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Attractors (Mathematics) | ||||
| Journal or Publication Title: | Proceedings of the American Mathematical Society | ||||
| Publisher: | American Mathematical Society | ||||
| ISSN: | 0002-9939 | ||||
| Official Date: | 2012 | ||||
| Dates: |
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| Date of first compliant deposit: | 20 December 2015 | ||||
| Volume: | Vol.140 | ||||
| Number: | No.7 | ||||
| Page Range: | pp. 2357-2373 | ||||
| DOI: | 10.1090/S0002-9939-2011-11071-2 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Funder: | Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil. Coordenação do Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) | ||||
| Grant number: | 302022/2008-2 (CNPq), 267/2008 (CAPES/DGU), 2008/55516-3 (FAPESP) |
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