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

TL;DR

This paper establishes the existence and regularity of pullback attractors for stochastic FitzHugh-Nagumo systems with additive noise on unbounded domains, using asymptotic a priori methods.

Contribution

It proves the existence of pullback attractors for non-autonomous stochastic FitzHugh-Nagumo systems with polynomial growth nonlinearities on unbounded domains, without requiring sign conditions.

Findings

Existence of pullback attractors in $L^{p}( ^N) imes L^{2}( ^N)$.

Asymptotic compactness proved via asymptotic a priori method.

Attractors accommodate polynomial nonlinearities without sign restrictions.

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.