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

Autor(es)

Caraballo, Tomas ^[1] ; Carvalho, Alexandre N. ^[2] ; Langa, Jose A. ^[1] ; Rivero, Felipe ^[1]

Afiliação do(s) autor(es)

^[1] Univ Seville, Dept Ecuac Diferenciales & Anal Numer, E-41080 Seville - Spain

^[2] Univ Sao Paulo, Inst Ciencias Matemat & Computacao, BR-13560970 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS; v. 74, n. 6, p. 2272-2283, MAR 15 2011.
• Citações Web of Science: 11

Resumo

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. (AU)

• Processo FAPESP: 08/53094-4 - Sistemas dinâmicos em espaços de dimensão infinita sob perturbações
• Beneficiário: Alexandre Nolasco de Carvalho
• Modalidade de apoio: Bolsas no Exterior - Pesquisa