Regularity of pullback random attractors for stochastic FitzHugh-Nagumo system on unbounded domains

Bao Quoc Tang

doi:10.3934/dcds.2015.35.441

Article Contents

2015, Volume 35, Issue 1: 441-466. Doi: 10.3934/dcds.2015.35.441

This issue Previous Article Infinitely many solutions for a Schrödinger-Poisson system with concave and convex nonlinearities Next Article On the quasi-periodic solutions of generalized Kaup systems

Regularity of pullback random attractors for stochastic FitzHugh-Nagumo system on unbounded domains

Bao Quoc Tang^1,

1.
Institute of Mathematics and Scientific Computing, University of Graz, 36 Heinrichstraβe, 8010 Graz

Received: October 31, 2013

Revised: April 30, 2014

Published: December 2014

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Abstract

The regularity of the pullback random attractor for a stochastic FitzHugh-Nagumo system on $\mathbb R^n$ driven by deterministic non-autonomous forcing is proved. More precisely, the pullback random attractor is shown to be compact in $H^1(\mathbb R^n)\times L^2(\mathbb R^n)$ and attract all tempered sets of $L^2(\mathbb R^n)\times L^2(\mathbb R^n)$ in the topology of $H^1(\mathbb R^n)\times L^2(\mathbb R^n)$. The proof is based on tail estimates technique, eigenvalues of the Laplace operator in bounded domains and some new estimates of solutions.

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Mathematics Subject Classification: Primary: 35B40, 35B41, 37L30, 37L55.

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