Continuity and topological structural stability for nonautonomous random attractors

In this work, we study the continuity and topological structural stability of attractors for nonautonomous random differential equations obtained by small bounded random perturbations of autonomous semilinear problems. First, we study the existence and permanence of unstable sets of hyperbolic solut...

Descripción completa

Detalles Bibliográficos
Autores: Caraballo Garrido, Tomás, Carvalho, Alexandre N., Langa Rosado, José Antonio, Oliveira Sousa, Alexandre N.
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2021
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/147927
Acceso en línea:https://hdl.handle.net/11441/147927
https://doi.org/10.1142/S021949372240024X
Access Level:acceso abierto
Palabra clave:Nonautonomous random dynamical systems
continuity of attractors
topological structural stability
bounded noise
damped wave equation
Descripción
Sumario:In this work, we study the continuity and topological structural stability of attractors for nonautonomous random differential equations obtained by small bounded random perturbations of autonomous semilinear problems. First, we study the existence and permanence of unstable sets of hyperbolic solutions. Then, we use this to establish the lower semicontinuity of nonautonomous random attractors and to show that the gradient structure persists under nonautonomous random perturbations. Finally, we apply the abstract results in a stochastic differential equation and in a damped wave equation with a perturbation on the damping.