Weak Pullback Mean Attractor for \(p\)-Laplacian Selkov Lattice Systems with Locally Lipschitz Delay Diffusion Terms
https://doi.org/10.61383/ejam.20231233
Keywords:
Nonlinear p-Laplacian, Weak pullback mean attractor, Selkov systems, Dalay time, Lipschitze noiseAbstract
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.
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Copyright (c) 2023 Yan Wang; Xiaolan Qin (Corresponding Author); Hailang Bai, Yu Wang
This work is licensed under a Creative Commons Attribution 4.0 International License.
Accepted 2023 Aug 06
Published 2023 Sep 09
