Weak mean random attractors for non-local random and stochastic reaction–diffusion equations

Abstract

In this paper, we prove the existence of weak pullback mean random attractors for a non-local stochastic reaction–diffusion equation with a nonlinear multiplicative noise. The existence and uniqueness of solutions and weak pullback mean random attractors are also established for a deterministic non-local reaction–diffusion equations with random initial data.

Long Time Behavior of Stochastic Nonlocal Partial Differential Equations and Wong--Zakai Approximations

“…In fact, when l is not a bounded linear operator as in our current case, for instance, when the functional l is given by l(u) = u 2 )∆u = f (u) + h(t), (t, x) ∈ (0, ∞) × O, u = 0, (t, x) ∈ (0, ∞) × ∂O, u(0, x) = u 0 (x), x ∈ O, were shown in [3]. Moreover, recently, the authors studied in [4] the existence and uniqueness of variational solution to the stochastic version of the above problem,…”