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arXiv · 2608.09319

Averaging Principle and Pullback Attractor Convergence for McKean--Vlasov Stochastic Reaction--Diffusion Equations

Honglei Chen·Mengyu Cheng·Zhenxin Liu
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Abstract

We establish three averaging principles for distribution-dependent stochastic reaction--diffusion equations with rapidly oscillating coefficients on the torus $\mathbb T^d$, $d\le3$. First, solutions converge in mean square, uniformly on finite time intervals, to solutions of the averaged equation. Under a contraction condition, both the original and averaged equations admit unique bounded entire solutions whose mean-square distance vanishes uniformly for all $t\in\mathbb R$. At the level of probability laws, the original nonautonomous equation possesses a family of pullback attractors, whereas the averaged equation has a global attractor; the former converge upper-semicontinuously to the latter, uniformly over the coefficient hull. As an application, we present a class of stochastic reaction--diffusion models motivated by large-scale interacting systems.

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Honglei Chen, Mengyu Cheng, Zhenxin Liu. 2026-08-10. Averaging Principle and Pullback Attractor Convergence for McKean--Vlasov Stochastic Reaction--Diffusion Equations. https://arxiv.org/abs/2608.09319

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