Equi-exponential attraction and rate of convergence of attractors with application to a perturbed damped wave equation

Autor(es)

Carvalho, Alexandre N. ^[1] ; Cholewa, Jan W. ^[2] ; Dlotko, Tomasz ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13560970 Sao Carlos, SP - Brazil

^[2] Silesian Univ, Inst Math, PL-40007 Katowice - Poland

• Tipo de documento: Artigo Científico
• Fonte: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS; v. 144, n. 1, p. 13-51, FEB 2014.
• Citações Web of Science: 2

Resumo

We consider a family of bounded dissipative asymptotically compact semigroups depending on a parameter, and study the continuity properties of the corresponding family of its global attractors. We exploit the idea of the uniform exponential attraction property to discuss the continuity properties of the family of attractors and estimate the rate of convergence of the approximating attractors to the limit one. Showing a range of applications of an abstract framework, we focus much of our attention on a perturbed damped wave equation. In this latter case our results involve nonlinearities with critical exponents, for which the continuity of the family of attractors is concluded, including the rate of convergence and the regularity of the limit attractor. This complements the results in the literature. (AU)

• Processo FAPESP: 09/52687-4 - Jan Wladyslaw Cholewa | University of Silesia - Polônia
• Beneficiário: Alexandre Nolasco de Carvalho
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional
• 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