Uniform attractors for a class of stochastic evolution equations with multiplicative fractional noise

Abstract

This paper studies the (random) uniform attractor for a class of non-autonomous stochastic evolution equations driven by a time-periodic forcing and multiplicative fractional noise with Hurst parameter bigger than 1/2. We first establish the existence and uniqueness results for the solution to the considered equation and show that the solution generates a jointly continuous non-autonomous random dynamical system (NRDS). Moreover, we prove the existence of the uniform attractor for this NRDS through stopping time technique. Particularly, a compact uniformly absorbing set is constructed under a smallness condition imposed on the fractional noise.