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

TL;DR

This paper establishes the existence of weak pullback mean random attractors for non-local stochastic reaction-diffusion equations with nonlinear noise, and also for deterministic equations with random initial data, advancing understanding of long-term behavior in such systems.

Contribution

It introduces the concept of weak pullback mean random attractors for non-local stochastic reaction-diffusion equations, including existence, uniqueness, and their relation to deterministic cases.

Findings

Existence of weak pullback mean random attractors for stochastic equations.

Uniqueness of solutions and attractors in the stochastic setting.

Extension of attractor theory to non-local reaction-diffusion equations with randomness.

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. Also, we establish the existence and uniqueness of solutions and weak pullback mean random attractors for a deterministic nonlocal reaction-diffusion equations with random initial data.