Dynamics of fractional stochastic Burgers–Huxley equation with Lévy noise

Abstract

This paper is mainly concerned with a fractional stochastic Burgers–Huxley equation with L$\acute{e}$vy noise in a bounded domain. We first state the well-posedness of the problem via iterative approximations and energy estimates in $L^2(\Omega ;D([0,T];L^2\left({\Re }^d\right)))\cap L^2(\Omega ;L^2(0.T;W^{\gamma ,2}\left({\Re }^d\right)))$. Then, the existence and uniqueness of weak pullback mean random attractors for the equations are established by defining a mean random dynamical system. Finally, we prove the existence of invariant measures for the fractional stochastic Burgers–Huxley equation with L$\acute{e}$vy noise.