Weak mean attractors of fractional stochastic lattice systems driven by nonlinear delay noise

Ailin Bai; Pengyu Chen

doi:10.61383/ejam.20242485

Authors

Ailin Bai Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
Pengyu Chen Department of Mathematics, Northwest Normal University, Lanzhou 730070, China Corresponding Author https://orcid.org/0000-0003-2891-4763

DOI:

https://doi.org/10.61383/ejam.20242485

Keywords:

Fractional stochastic lattice system, nonlinear delay noise, weak mean random attractor

Abstract

This paper deals with the existence and uniqueness of weak pullback mean random attractors for fractional stochastic lattice systems driven by nonlinear delay noise defined on the entire integer set \(\mathbb{Z}\). We first establish the global well-posedness to stochastic lattice system in \(C([\tau,\infty), L^2(\Omega, \ell^2))\) when the nonlinear diffusion terms and drift terms are locally Lipschitz continuous functions. Then we define a mean random dynamical system through the solution operators and prove the existence and uniqueness of weak pullback mean random attractors in \(L^2(\Omega,\mathcal{F};\ell^2)\times L^2\big(\Omega,\mathcal{F};L^2((-\rho,0), \ell^2)\big)\) under certain conditions.

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