Abstract
This article concerns bi-spatial random dynamics for the stochastic reaction-diffusion equation on a thin domain, where the noise is described by a general stochastic process instead of the usual Wiener process. A bi-spatial attractor is obtained when the non-initial state space is the $p$-times Lebesgue space, meanwhile, measurability of the attractor in the Banach space is proved by using measurability of both cocycle and absorbing set. Finally, the $p$-norm convergence of attractors is obtained when the thin domain collapses onto a lower dimensional domain. The method of symbolical truncation is applied to provide some uniformly asymptotic estimates.
Citation
Fuzhi Li. Yangrong Li. Renhai Wang. "Strong convergence of bi-spatial random attractors for parabolic equations on thin domains with rough noise." Topol. Methods Nonlinear Anal. 53 (2) 659 - 682, 2019. https://doi.org/10.12775/TMNA.2019.015