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arXiv · 2511.00572

Long-term behavior of nonlocal reaction-diffusion equation under small random perturbations

Xiuling Gui·Jin Yang·Chunfeng Wang·Jing Hou·Ji Shu
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Abstract

In this paper, we investigate the nonlocal reaction-diffusion equation driven by stationary noise, which is a regular approximation to white noise and satisfies certain properties. We show the existence of random attractor for the equation. When stochastic nonlocal reaction-diffusion equation is driven by additive and multiplicative noise, we prove that the solution converges to the corresponding deterministic equation and establish the upper semicontinuity of the attractors as the perturbation parameter \delta and \epsilon both approaches zero.

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Xiuling Gui, Jin Yang, Chunfeng Wang, Jing Hou, Ji Shu. 2025-11-01. Long-term behavior of nonlocal reaction-diffusion equation under small random perturbations. https://arxiv.org/abs/2511.00572

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