Dynamics of a stochastic fractional nonlocal reaction-diffusion model driven by additive noise

In this paper, we are concerned with the long-time behavior of stochastic fractional nonlocal reaction-diffusion equations driven by additive noise. We use the techniques of random dynamical systems to transform the stochastic model into a random one. To deal with the new nonlocal term appeared in t...

Full description

Bibliographic Details
Authors: Li, Lingyu, Chen, Zhang, Caraballo Garrido, Tomás
Format: article
Status:Versión enviada para evaluación y publicación
Publication Date:2022
Country:España
Institution:Universidad de Sevilla (US)
Repository:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/150165
Online Access:https://hdl.handle.net/11441/150165
https://doi.org/10.3934/dcdss.2022179
Access Level:Open access
Keyword:Stochastic fractional nonlocal reaction-diffusion equation
additive noise
random attractor
colored noise
upper semi-continuity
Description
Summary:In this paper, we are concerned with the long-time behavior of stochastic fractional nonlocal reaction-diffusion equations driven by additive noise. We use the techniques of random dynamical systems to transform the stochastic model into a random one. To deal with the new nonlocal term appeared in the transformed equation, we first use a generalization of Peano’s theorem to prove the existence of local solutions, and then adopt the Galerkin method to prove existence and uniqueness of weak solutions. Next, the existence of pullback attractors for the equation and its associated Wong-Zakai approximation equation driven by colored noise are shown, respectively. Furthermore, we establish the upper semi-continuity of random attractors of the Wong-Zakai approximation equation as δ → 0 +.