RANDOM ATTRACTORS FOR NON-AUTONOMOUS FRACTIONAL STOCHASTIC PARABOLIC EQUATIONS ON UNBOUNDED DOMAINS

摘要

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 R-n. We first prove the pathwise well-posedness of the equation and define a continuous non-autonomous cocycle in L-2(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(R-n) is established by the uniform estimates on the tails of solutions for sufficiently large space and time variables.