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

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.

💡 Research Summary

This paper investigates the long‑time behavior of a class of non‑local reaction‑diffusion equations both in deterministic and stochastic settings. The authors focus on the existence of weak pullback mean random attractors—objects that capture the asymptotic dynamics in a probabilistic sense when the underlying system is driven by random influences.

The work builds on the theory of weak mean‑square random attractors introduced in previous literature (particularly reference