THE EXISTENCE OF RANDOM <inline-formula><tex-math id="M1">$\mathcal{D}$</tex-math></inline-formula>-PULLBACK ATTRACTORS FOR RANDOM DYNAMICAL SYSTEM AND ITS APPLICATIONS

Abstract

In this paper, we establish a result on the existence of random $\mathcal{D}$-pullback attractors for norm-to-weak continuous non-autonomous random dynamical system. Then we give a method to prove the existence of random $\mathcal{D}$-pullback attractors. As an application, we prove that the non-autonomous stochastic reaction diffusion equation possesses a random $\mathcal{D}$-pullback attractor in $H_0^1$ with polynomial growth of the nonlinear term.