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

By Yangrong Li, Jinyan Yin. 2016

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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.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c0fd9adec6fccf47e520264360d06ab44e9d89e9