Biblioteca de la Universidad Complutense de Madrid

Continuity of Dynamical Structures for Nonautonomous Evolution Equations Under Singular Perturbations

Impacto

Arrieta Algarra, José María y Carvalho, Alexandre N. y Langa, José A. y Rodríguez Bernal, Aníbal (2012) Continuity of Dynamical Structures for Nonautonomous Evolution Equations Under Singular Perturbations. Journal of Dynamics and Differential Equations, 24 (3). pp. 427-481. ISSN 1040-7294

[img] PDF
Restringido a Sólo personal autorizado del repositorio hasta 31 Diciembre 2020.

626kB

URL Oficial: http://www.springerlink.com/content/1411835408267004/fulltext.pdf




Resumen

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.


Tipo de documento:Artículo
Palabras clave:Nonautonomous dynamical systems; Hyperbolic global bounded solutions; Unstable manifolds; Dichotomy; Singular perturbations; Attractors; Lower semicontinuity
Materias:Ciencias > Matemáticas > Ecuaciones diferenciales
Código ID:16761
Depositado:18 Oct 2012 11:02
Última Modificación:07 Feb 2014 09:35

Sólo personal del repositorio: página de control del artículo