Weak Pullback Mean Random Attractors for Stochastic Evolution Equations and Applications

TL;DR

This paper establishes the existence and uniqueness of weak pullback mean random attractors for a class of stochastic evolution equations, with applications to various stochastic PDE models.

Contribution

It introduces new results on weak pullback mean random attractors for stochastic evolution equations with general diffusion terms, extending previous work in the field.

Findings

Existence and uniqueness of attractors for stochastic reaction-diffusion equations

Existence and uniqueness for stochastic p-Laplace equations

Results applicable to stochastic porous media equations

Abstract

In this paper, we investigate the existence and uniqueness of weak pullback mean random attractors for abstract stochastic evolution equations with general diffusion terms in Bochner spaces. As applications, the existence and uniqueness of weak pullback mean random attractors for some stochastic models such as stochastic reaction-diffusion equations, the stochastic $p$-Laplace equation and stochastic porous media equations are established.