Dynamics of a Stochastic Fractional Reaction-Diffusion Equation

Abstract

In this paper, we study the dynamics of a stochastic fractional reaction-diffusion equation with multiplicative noise in three spatial dimension. By proving the well-posedness and conducting a priori estimates for the solutions of the considered equation we obtain simultaneously the existence and the regularity of random attractors of the random dynamical systems for the equation. The main approach here is to establish an abstract result on existence of bi-spatial random attractors for random dynamical systems. Moreover, we also give estimate of the Hausdorff dimension in $L^{2}$ space for the obtained random attractor.