Artículo
A gradient-like non autonomous evolution process
Autor/es | Caraballo Garrido, Tomás
Langa Rosado, José Antonio Rivero Garvía, Luis Felipe Carvalho, Alexandre Nolasco |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2009 |
Fecha de depósito | 2015-04-27 |
Publicado en |
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Resumen | 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 ... 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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