Random attractors for non-autonomous fractional stochastic parabolic equations on unbounded domains

Abstract

We study the asymptotic behavior of a class of non-autonomous non-local fractional stochastic parabolic equation driven by multiplicative white noise on the entire space $\mathbb{R}^n$. We first prove the pathwise well-posedness of the equation and define a continuous non-autonomous cocycle in $L^2({\mathbb{R}} ^n)$. We then prove the existence and uniqueness of tempered pullback attractors for the cocycle under certain dissipative conditions. The periodicity of the tempered attractors is also proved when the deterministic non-autonomous external terms are periodic in time. The pullback asymptotic compactness of the cocycle in $L^2({\mathbb{R}} ^n)$ is established by the uniform estimates on the tails of solutions for sufficiently large space and time variables.