Strong convergence of bi-spatial random attractors for parabolic equations on thin domains with rough noise

Fuzhi Li, Yangrong Li, Renhai Wang



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.


Bi-spatial random attractor; stochastic reaction-diffusion equation; rough noise; thin domain; strong semi-continuity; regularity; symbolical truncation

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