Strong convergence of bi-spatial random attractors for parabolic equations on thin domains with rough noise
Keywords
Bi-spatial random attractor, stochastic reaction-diffusion equation, rough noise, thin domain, strong semi-continuity, regularity, symbolical truncationAbstract
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.References
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