RT Journal Article
T1 Continuity of Dynamical Structures for Nonautonomous Evolution Equations Under Singular Perturbations
A1 Arrieta Algarra, José María
A1 Carvalho, Alexandre N.
A1 Langa, José A.
A1 Rodríguez Bernal, Aníbal
AB 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.
PB Springer
SN 1040-7294
YR 2012
FD 2012-09
LK https://hdl.handle.net/20.500.14352/42346
UL https://hdl.handle.net/20.500.14352/42346
LA eng
NO MICINN
NO UCM-BCSH
NO MICINN
NO CNPq
NO FAFESP, Brazil
NO FEDER, Spain
DS Docta Complutense
RD 27 jul 2024