Regularity of pullback attractors and equilibrium for non-autonomous stochastic FitzHugh-Nagumo system on unbounded domains

2014/12/03 by Zhao, Wenqiang, Gu, Anhui
#35B40 #35B41 #35R60 #60H15 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1412.1160

Abstract

A theory on bi-spatial random attractors developed recently by Li et al. is extended to study stochastic Fitzhugh-Nagumo system driven by a non-autonomous term as well as a general multiplicative noise. By using the so-called notions of uniform absorption and uniformly pullback asymptotic compactness, it is showed that every generated random cocycle has a pullback attractor in L^l(ℝ^N)× L²(ℝ^N) with l∈(2,p], and the family of obtained attractors is upper semi-continuous at any intensity of noise. Moreover, if some additional conditions are added, then the system possesses a unique equilibrium and is attracted by a single point.

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