Random attractors for stochastic retarded reaction-diffusion equations with multiplicative white noise on unbounded domains

Abstract

Abstract In this paper we investigate the stochastic retarded reaction-diffusion equations with multiplicative white noise on unbounded domain ℝ n (n ≥ 2). We first transform the retarded reaction-diffusion equations into the deterministic reaction-diffusion equations with random parameter by Ornstein-Uhlenbeck process. Next, we show the original equations generate the random dynamical systems, and prove the existence of random attractors by conjugation relation between two random dynamical systems. In this process, we use the cut-off technique to obtain the pullback asymptotic compactness.