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| Full text | |
| Author(s): |
Arrieta, Jose M.
[1]
;
Carvalho, Alexandre N.
[2]
;
Langa, Jose A.
[3]
;
Rodriguez-Bernal, Anibal
[1]
Total Authors: 4
|
| Affiliation: | [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
Total Affiliations: 3
|
| Document type: | Journal article |
| Source: | Journal of Dynamics and Differential Equations; v. 24, n. 3, p. 427-481, SEP 2012. |
| Web of Science Citations: | 2 |
| Abstract | |
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) | |
| FAPESP's process: | 03/10042-0 - Nonlinear dynamical systems and applications |
| Grantee: | Alexandre Nolasco de Carvalho |
| Support Opportunities: | PRONEX Research - Thematic Grants |