Dynamics of stochastic nonlocal reaction-diffusion equations driven by multiplicative noise

This paper deals with fractional stochastic nonlocal partial differential equations driven by multiplicative noise. We first prove the existence and uniqueness of solution to this kind of equations with white noise by applying the Galerkin method. Then, the existence and uniqueness of tempered pullb...

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Detalles Bibliográficos
Autores: Xu, Jiaohui, Caraballo Garrido, Tomás
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2022
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/147898
Acceso en línea:https://hdl.handle.net/11441/147898
https://doi.org/10.1142/S0219530522500075
Access Level:acceso abierto
Palabra clave:Fractional stochastic nonlocal PDEs
Multiplicative noise
Random attractors
Colored noise
Upper semicontinuity
Wong-Zakai approximations
Descripción
Sumario:This paper deals with fractional stochastic nonlocal partial differential equations driven by multiplicative noise. We first prove the existence and uniqueness of solution to this kind of equations with white noise by applying the Galerkin method. Then, the existence and uniqueness of tempered pullback random attractor for the equation are ensured in an appropriate Hilbert space. When the fractional nonlocal partial differential equations are driven by colored noise, which indeed are approximations of the previous ones, we show the convergence of solutions of Wong-Zakai approximations and the upper semicontinuity of random attractors of the approximate random system as δ → 0.