Regularity of pullback attractors for non-autonomous stochastic FitzHugh-Nagumo systems with additive noises on unbounded domains

Abstract

In this paper, we prove the existences of pullback attractors in $L^p({\mathbb{R}}^N)\times L^2({\mathbb{R}}^N)$ for stochastic Fitzhugh-Nagumo system driven by both additive noises and deterministic non-autonomous forcings. The nonlinearity is polynomial like growth with exponent $p-1$. The asymptotic compactness for the cocycle in $L^p({\mathbb{R}}^N)\times L^2({\mathbb{R}}^N)$ is proved by using asymptotic a priori method, where the plus and minus signs of the nonlinearity at large value are not required.