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Artículo
A gradient-like non autonomous evolution process
dc.creator | Caraballo Garrido, Tomás | |
dc.creator | Langa Rosado, José Antonio | |
dc.creator | Rivero Garvía, Luis Felipe | |
dc.creator | Carvalho, Alexandre Nolasco | |
dc.date.accessioned | 2015-04-27T07:30:06Z | |
dc.date.available | 2015-04-27T07:30:06Z | |
dc.date.issued | 2009 | |
dc.identifier.uri | http://hdl.handle.net/11441/24705 | |
dc.description.abstract | In this paper we consider a dissipative damped wave equation with non-autonomous damping of the form utt + ¯(t)ut = ¢u + f(u) (1) in a bounded smooth domain ½ Rn with Dirichlet boundary conditions, where f is a dissipative smooth nonlinearity and the damping ¯ : R ! (0;1) is a suitable function. We prove, if (1) has finitely many equilibria, that all global bounded solutions of (1) are backwards and forwards asymptotic to equilibria. Thus, we give a class of examples of non-autonomous evolution processes for which the structure of the pullback attractors is well understood. That complements the results of [Carvalho & Langa, 2009] on characterization of attractors, where it was shown that a small non-autonomous perturbation of an autonomous gradient-like evolution process is also gradient-like. Note that the evolution process associated to (1) is not a small non-autonomous perturbation of any autonomous gradient-like evolution processes. Moreover, we are also able to prove that the pullback attractor for (1) is also a forwards attractor and that the rate of attraction is exponential. | es |
dc.format | application/pdf | es |
dc.language.iso | eng | es |
dc.relation.ispartof | Notas. Série Matemática, 304, 1-15 | es |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Pullback attractor | es |
dc.subject | asymptotic compactness | es |
dc.subject | evolution process | es |
dc.subject | non-autonomous damped wave equation | es |
dc.title | A gradient-like non autonomous evolution process | es |
dc.type | info:eu-repo/semantics/article | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico | es |
dc.identifier.idus | https://idus.us.es/xmlui/handle/11441/24705 |
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