Pullback attractors of FitzHugh-Nagumo system on the time-varying domains

Zhen Zhang; Jianhua Huang; Xueke Pu

doi:10.3934/dcdsb.2017150

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2017, Volume 22, Issue 10: 3691-3706. Doi: 10.3934/dcdsb.2017150

This issue Previous Article Area preserving geodesic curvature driven flow of closed curves on a surface Next Article Dynamical behaviors of a generalized Lorenz family

Pullback attractors of FitzHugh-Nagumo system on the time-varying domains

1.
College of Science, National University of Defense Technology, Changsha 410073, China
2.
College of Mathematics and Statistics, Chongqing University, Chongqing 400044, China

* Corresponding author: Jianhua Huang
* Corresponding author: Jianhua Huang

Received: December 2016

Revised: January 2017

Published: September 2017

The authors are supported by the NSF of China(No.11371367,11571126), the third author is also supported by the Fundamental Research Funds for the Central Universities (106112016CDJZR105501).

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Abstract

The existence and uniqueness of solutions satisfying energy equality is proved for non-autonomous FitzHugh-Nagumo system on a special time-varying domain which is a (possibly non-smooth) domain expanding with time. By constructing a suitable penalty function for the two cases respectively, we establish the existence of a pullback attractor for non-autonomous FitzHugh-Nagumo system on a special time-varying domain.

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Mathematics Subject Classification: Primary:35K57, 35K90;Secondary:37L30.

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