Asymptotic Autonomy of Attractors for Stochastic Fractional Nonclassical Diffusion Equations Driven by a Wong–Zakai Approximation Process on ℝ^<i>n</i>

Abstract

In this paper, we consider the backward asymptotically autonomous dynamical behavior for fractional non-autonomous nonclassical diffusion equations driven by a Wong–Zakai approximations process in Hs(Rn) with s∈(0,1). We first prove the existence and backward time-dependent uniform compactness of tempered pullback random attractors when the growth rate of nonlinearities have a subcritical range. We then show that, under the Wong–Zakai approximations process, the components of the random attractors of a non-autonomous dynamical system in time can converge to those of the random attractor of the limiting autonomous dynamical system in Hs(Rn).

Keywords

• fractional nonclassical diffusion equation
• Wong–Zakai approximations
• random attractor
• asymptotically autonomous