Wong–Zakai approximations and attractors for stochastic degenerate parabolic equations on unbounded domains

Abstract

The Wong–Zakai approximations given by a stationary process and attractors for stochastic degenerate parabolic equations are considered in this paper. We first establish the existence and uniqueness of tempered pullback attractors for the Wong–Zakai approximations of stochastic degenerate parabolic equations. We then prove that the attractors of Wong–Zakai approximations converge to the attractor of stochastic degenerate parabolic equations driven by multiplicative white noise.