TY - JOUR
AU - Wang, Yan
AU - QIN, Xiaolan
AU - Bai, Hailang
AU - Wang, Yu
PY - 2023/09/09
Y2 - 2024/03/01
TI - Weak Pullback Mean Attractor for \(p\)-Laplacian Selkov Lattice Systems with Locally Lipschitz Delay Diffusion Terms
JF - Electronic Journal of Applied Mathematics
JA - Electron. J. Appl. Math.
VL - 1
IS - 2
SE - Research Article
DO - 10.61383/ejam.20231233
UR - https://ejamjournal.com/index.php/ejam/article/view/ejam.20231233
SP - 1-17
AB - <p>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.</p>
ER -