Advanced search
Start date
Betweenand
Related content
(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

Full text
Author(s):
Caraballo, Tomas [1] ; Carvalho, Alexandre N. [2] ; Langa, Jose A. [1] ; Rivero, Felipe [1]
Total Authors: 4
Affiliation:
[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
Total Affiliations: 2
Document type: Journal article
Source: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS; v. 74, n. 6, p. 2272-2283, MAR 15 2011.
Web of Science Citations: 11
Abstract

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)