Wong-Zakai approximations and random attractors for non-autonomous stochastic lattice systems

By Xiaohu Wang, Jun Shen, Kening Lu, Bixiang Wang. Journal of Differential Equations, 2021

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Abstract In this paper, we study the Wong-Zakai approximations given by a stationary process via the Wiener shift and their associated long term pathwise behavior for the stochastic lattice systems. We first prove that the approximate system has a unique tempered pullback attractor under much weaker conditions than the original system. When the stochastic system is driven by a linear multiplicative noise or additive white noise, we prove the convergence of solutions and the upper semicontinuity of random attractors for Wong-Zakai approximations as the step-length of the Wiener shift approaches zero.

Subfields: Computational Theory and Mathematics, Computer Networks and Communications, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/d8b400406d94f4e76f5338b9ff11c1ff6925c9fc