Long time behavior of stochastic parabolic problems with white noise in materials with thermal memory

The existence and limiting behavior of the solutions of stochastic parabolic problems with thermal memory are investigate in the cases that the nonlinear term satisfies subcritical and critical growth conditions. The existence, uniqueness and continuity of solutions is proved by a semigroup method a...

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Detalles Bibliográficos
Autores: Liu, Linfang, Caraballo Garrido, Tomás, Kloeden, Peter E.
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2017
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/67405
Acceso en línea:http://hdl.handle.net/11441/67405
https://doi.org/10.1007/s13163-017-0238-1
Access Level:acceso abierto
Palabra clave:Parabolic equation with memory
Pullback random attractor
Critical nonlinearity
Semigroup method
Upper semi-continuity
Descripción
Sumario:The existence and limiting behavior of the solutions of stochastic parabolic problems with thermal memory are investigate in the cases that the nonlinear term satisfies subcritical and critical growth conditions. The existence, uniqueness and continuity of solutions is proved by a semigroup method and the Lax-Milgram theorem, then the dynamics of solutions is analyzed by a priori estimates. In particular, the existence of pullback random attractors for the random dynamical system associated to the problem is established and the upper semi-continuity of the pullback random attractors is verified.