Three types of weak pullback attractors for lattice pseudo-parabolic equations driven by locally Lipschitz noise

Abstract

<p style='text-indent:20px;'>The global well-posedness and long-time mean random dynamics are studied for a high-dimensional non-autonomous stochastic nonlinear lattice pseudo-parabolic equation with <i>locally</i> Lipschitz drift and diffusion terms. The existence and uniqueness of three different types of weak pullback mean random attractors as well as their relations are established for the mean random dynamical systems generated by the solution operators. This is the first paper to study the well-posedness and dynamics of the stochastic lattice pseudo-parabolic equation even when the nonlinear noise reduces to the linear one.</p>