Weak Pullback Mean Attractor for \(p\)-Laplacian Selkov Lattice Systems with Locally Lipschitz Delay Diffusion Terms

作者：Yan Wang, Xiaolan Qin, Hailang Bai, Yu Wang · 发表于：Electronic Journal of Applied Mathematics · 年份：2023 · DOI：10.61383/ejam.20231233 · 被引用次数：4 · 研究领域：Stability and Controllability of Differential Equations、Advanced Mathematical Modeling in Engineering、Nonlinear Differential Equations Analysis

This paper focuses on the dynamics of a class of nonlinear, reversible, random \(p\)-Laplace Selkov delay lattice systems defined by local lipschitz noise-driven \(\mathbb{Z}^d\). We first establish the global fitness of the system using the local Lipschitz delayed diffusion term. Under certain conditions, we demonstrate the existence and uniqueness of the mean stochastic dynamical system in relation to the stochastic equation in the product Hilbert space \(L^2(\Omega, \mathcal{F}_\tau; \ell^2\times\ell^2） \times L^2 （\Omega， \mathcal{F}_\tau; L^2((-\rho, 0), \ell^2\times\ell^2) \). The average stochastic dynamical system theory proposed by Wang (J.Equ., 31:2177-2204, 2019) is used to deal with the difficulties caused by nonlinear noise. Even if the discrete \(p\)-Laplace is replaced by the usual discrete Laplace, the results of this paper are new.