Continuity of Dynamical Structures for Nonautonomous Evolution Equations Under Singular Perturbations

Autor(es)

Arrieta, Jose M. ^[1] ; Carvalho, Alexandre N. ^[2] ; Langa, Jose A. ^[3] ; Rodriguez-Bernal, Anibal ^[1]

Afiliação do(s) autor(es)

^[1] Univ Complutense Madrid, Fac Matemat, Dept Matemat Aplicada, E-28040 Madrid - Spain

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

^[3] Univ Seville, Dept Ecuac Diferenciales & Anal Numer, E-41012 Seville - Spain

• Tipo de documento: Artigo Científico
• Fonte: Journal of Dynamics and Differential Equations; v. 24, n. 3, p. 427-481, SEP 2012.
• Citações Web of Science: 2

Resumo

In this paper we study the continuity of invariant sets for nonautonomous infinite-dimensional dynamical systems under singular perturbations. We extend the existing results on lower-semicontinuity of attractors of autonomous and nonautonomous dynamical systems. This is accomplished through a detailed analysis of the structure of the invariant sets and its behavior under perturbation. We prove that a bounded hyperbolic global solutions persists under singular perturbations and that their nonlinear unstable manifold behave continuously. To accomplish this, we need to establish results on roughness of exponential dichotomies under these singular perturbations. Our results imply that, if the limiting pullback attractor of a nonautonomous dynamical system is the closure of a countable union of unstable manifolds of global bounded hyperbolic solutions, then it behaves continuously (upper and lower) under singular perturbations. (AU)

• Processo FAPESP: 03/10042-0 - Sistemas dinâmicos não lineares e aplicações
• Beneficiário: Alexandre Nolasco de Carvalho
• Linha de fomento: Auxílio à Pesquisa - Programa PRONEX - Temático