On The Relation Between Two Different Concepts of Pullback Attractors for Non-Autonomous Dynamical Systems

For an abstract dynamical system, we establish, under minimal assumptions, the existence of D-attractor, i.e. a pullback attractor for a given class D of families of time varying subsets of the phase space. We relate this concept with the usual attractor of fixed bounded sets, pointing out its usefu...

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Detalles Bibliográficos
Autores: Marín Rubio, Pedro, Real Anguas, José
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2009
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/25936
Acceso en línea:http://hdl.handle.net/11441/25936
https://doi.org/10.1016/j.na.2009.02.065
Access Level:acceso abierto
Palabra clave:Pullback attractors
Non-autonomous dynamical systems
Tempered sets
Descripción
Sumario:For an abstract dynamical system, we establish, under minimal assumptions, the existence of D-attractor, i.e. a pullback attractor for a given class D of families of time varying subsets of the phase space. We relate this concept with the usual attractor of fixed bounded sets, pointing out its usefulness in order to ensure the existence of this last attractor in particular situations. Moreover, we prove that under a simple assumption these two notions of attractors generate, in fact, the same object. This is then applied to a Navier–Stokes model, improving some previous results on attractor theory.