A non-autonomous strongly damped wave equation: Existence and continuity of the pullback attractor

In this paper we consider the strongly damped wave equation with time-dependent terms u(tt) - Delta u - gamma(t)Delta u(t) + beta(epsilon)(t)u(t) = f(u), in a bounded domain Omega subset of R(n), under some restrictions on beta(epsilon)(t), gamma(t) and growth restrictions on the nonlinear term f. The function beta(epsilon)(t) depends on a parameter epsilon, beta(epsilon)(t) -> 0. We will prove, under suitable assumptions, local and global well-posedness (using the uniform sectorial operators theory), the existence and regularity of pullback attractors {A(epsilon)(t) : t is an element of R}, uniform bounds for these pullback attractors, characterization of these pullback attractors and their upper and lower semicontinuity at epsilon = 0. (C) 2010 Elsevier Ltd. All rights reserved.

Ministerio de Ciencia e Innovacion[MTM2008-0088]

Ministerio de Ciencia e Innovacion

Junta de Andalucia (Spain)

Junta de Andalucia, Spain[P07-FQM-02468]

Junta de Andalucia, Spain[FQM314]

Junta de Andalucia (Spain)

Junta de Andalucia, Spain[HF2008-0039]

Junta de Andalucia (Spain)

CNPq[305447/2005-0]

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

CNPq[451761/2008-1]

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

CAPES/DGU[267/2008]

DGU

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

FAPESP, Brazil[2008/53094-4]

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)