Regularity and continuity of pullback attractors for non-autonomous stochastic FitzHugh-Nagumo systems on unbounded domains

Wenqiang Zhao

Published 2014-12-03Version 1

In this paper, we prove the existences and uniqueness of pullback attractors in $L^{\varpi}(\mathbb{R}^N)\times L^{2}(\mathbb{R}^N)$ for stochastic Fitzhugh-Nagumo systems driven by a multiplicative noise and a deterministic non-autonomous forcing. The upper semi-continuity of the perturbed random attractors in $L^{\varpi}(\mathbb{R}^N)\times L^{2}(\mathbb{R}^N)$ is proved when the intension of noise approaches any nonnegative number, where $\varpi\in[2,p]$.