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

Hong Lu; Jiangang Qi; Bixiang Wang; Mingji Zhang

doi:10.3934/dcds.2019028

Article Contents

2019, Volume 39, Issue 2: 683-706. Doi: 10.3934/dcds.2019028

This issue Previous Article Stochastic dominance for shift-invariant measures Next Article Planar S-systems: Global stability and the center problem

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

1.
School of Mathematics and Statistics, Shandong University, Weihai, Shandong Provence, 264209, China
2.
Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA

Received: April 2017

Revised: January 2018

Published: February 2019

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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.

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Mathematics Subject Classification: Primary: 35B40; Secondary: 35B41, 37L30.

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