A gradient-like non autonomous evolution process
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. W...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2009 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/24705 |
| Acceso en línea: | http://hdl.handle.net/11441/24705 |
| Access Level: | acceso abierto |
| Palabra clave: | Pullback attractor asymptotic compactness evolution process non-autonomous damped wave equation |
| Sumario: | 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. |
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