Wong–Zakai approximations for non-autonomous stochastic parabolic equations with X-elliptic operators in higher regular spaces

Abstract

In this paper, we consider the regularity of Wong–Zakai approximations of the non-autonomous stochastic degenerate parabolic equations with X-elliptic operators. We first establish the pullback random attractors for the random degenerate parabolic equations with a general diffusion. Then, we prove the convergence of solutions and the upper semi-continuity of random attractors of the Wong–Zakai approximation equations in L p( D N) ∩ H.