A modified  proof of pullback attractors in a Sobolev space for stochastic FitzHugh-Nagumo equations

Yangrong  Li; Jinyan  Yin

doi:10.3934/dcdsb.2016.21.1203

Article Contents

2016, Volume 21, Issue 4: 1203-1223. Doi: 10.3934/dcdsb.2016.21.1203

This issue Previous Article Analysis of a non-autonomous mutualism model driven by Levy jumps Next Article Dynamic transitions of generalized Kuramoto-Sivashinsky equation

A modified proof of pullback attractors in a Sobolev space for stochastic FitzHugh-Nagumo equations

Yangrong Li^1, and
Jinyan Yin^1,

1.
School of Mathematics and Statistics, Southwest University, Chongqing 400715

Received: May 31, 2015

Published: May 2016

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Abstract

A bi-spatial pullback attractor is obtained for non-autonomous and stochastic FitzHugh-Nagumo equations when the initial space is $L^2(\mathbb{R}^n)^2$ and the terminate space is $H^1(\mathbb{R}^n)\times L^2(\mathbb{R}^n)$. Some new techniques of positive and negative truncations are used to investigate the regularity of attractors for coupling equations and to correct the essential mistake in [T. Q. Bao, Discrete Cont. Dyn. Syst. 35(2015), 441-466]. A counterexample is given for an important lemma for $H^1$-attractor in several literatures included above.

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Mathematics Subject Classification: Primary: 37L55; Secondary: 35B41, 35R60.

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