Uniform measure attractors for nonautonomous stochastic lattice wave equations with delay driven by nonlinear noise

Abstract

In this paper, we investigate the existence and structure of uniform measure attractors for nonautonomous stochastic lattice wave equations with delay, driven by nonlinear noise and subject to almost periodic external forces. Since the presence of nonlinear noise and almost periodic external forcing renders the random attractors of classical random dynamical systems inapplicable, we employ the skew-product flow approach to establish the existence of uniform measure attractors for nonautonomous stochastic lattice wave equations with delay under the combined effects of nonlinear noise and almost periodic forcing. Notably, the tail-estimate technique is applied to prove the uniform asymptotic compactness of the family of processes generated by solution operators.