Random pullback attractor of a non-autonomous local modified stochastic Swift–Hohenberg equation with multiplicative noise

Abstract

In this paper, we study the existence of the random D-pullback attractor of a non-autonomous local modified stochastic Swift–Hohenberg equation with multiplicative noise in the Stratonovich sense. We show that a random D-pullback attractor exists in H02(D) when its external force has exponential growth. Due to the stochastic term, a priori estimates are delicate. We used the Ornstein–Uhlenbeck transformation and its properties to overcome the difficulty that the stochastic term brings to us.