Random attractors for locally monotone stochastic partial differential equations with linear multiplicative fractional noise

Abstract

In this paper, we consider the random attractors for a class of locally monotone stochastic partial differential equations perturbed by the linear multiplicative fractional Brownian motion with Hurst index $H\in (\frac{1}{2},1)$. We obtain the random attractors or $\mathcal{D}$-pullback random attractors for these systems and some examples are given in this paper.