2015-04-272015-04-272009http://hdl.handle.net/11441/24705In 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.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Pullback attractorasymptotic compactnessevolution processnon-autonomous damped wave equationinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://idus.us.es/xmlui/handle/11441/24705