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arXiv · 2610.16388

$\mathcal{D}$-Pullback Measure Attractors of McKean-Vlasov Stochastic Lattice Wave Equations

Huixia Wen·Ji Shu·Gang He
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Abstract

This paper deals with the pullback measure attractor for a non-autonomous distribution-dependent stochastic lattice wave equation with nonlinear noise on $\mathbb{Z}$. We establish well-posedness in the energy space $\ell^{2}\times\ell^{2}$ and show that the solution generates a continuous non-autonomous dynamical system on $\mathcal{P}_{4}(\ell^{2}\times\ell^{2})$, which possesses a unique pullback measure attractor $\mathcal{A}$. Furthermore, we prove the convergence of the attractor $\mathcal{A}^{\varepsilon}$ as $\varepsilon\to 0^{+}$ to the attractor of the corresponding distribution-independent limit system.

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Huixia Wen, Ji Shu, Gang He. 2026-10-12. $\mathcal{D}$-Pullback Measure Attractors of McKean-Vlasov Stochastic Lattice Wave Equations. https://arxiv.org/abs/2610.16388

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