A GRADIENT-LIKE NONAUTONOMOUS EVOLUTION PROCESS
Contribuinte(s) |
UNIVERSIDADE DE SÃO PAULO |
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Data(s) |
20/10/2012
20/10/2012
2010
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Resumo |
In this paper we consider a dissipative damped wave equation with nonautonomous damping of the form u(tt) + beta(t)u(t) - Delta u + f(u) (1) in a bounded smooth domain Omega subset of R(n) with Dirichlet boundary conditions, where f is a dissipative smooth nonlinearity and the damping beta : R -> (0, infinity) 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 nonautonomous 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 nonautonomous perturbation of an autonomous gradient-like evolution process is also gradient-like. Note that the evolution process associated to (1) is not a small nonautonomous 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. |
Identificador |
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v.20, n.9, p.2751-2760, 2010 0218-1274 http://producao.usp.br/handle/BDPI/28817 10.1142/S0218127410027337 |
Idioma(s) |
eng |
Publicador |
WORLD SCIENTIFIC PUBL CO PTE LTD |
Relação |
International Journal of Bifurcation and Chaos |
Direitos |
restrictedAccess Copyright WORLD SCIENTIFIC PUBL CO PTE LTD |
Palavras-Chave | #Pullback attractor #asymptotic compactness #evolution process #nonautonomous damped wave equation #EQUATIONS #Mathematics, Interdisciplinary Applications #Multidisciplinary Sciences |
Tipo |
article proceedings paper publishedVersion |