A Heteroclinic Solution to a Variational Problem Corresponding to FitzHugh-Nagumo type Reaction-Diffusion System with Heterogeneity

Takashi Kajiwara

doi:10.3934/cpaa.2017106

Article Contents

2017, Volume 16, Issue 6: 2133-2156. Doi: 10.3934/cpaa.2017106

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A Heteroclinic Solution to a Variational Problem Corresponding to FitzHugh-Nagumo type Reaction-Diffusion System with Heterogeneity

Takashi Kajiwara

Department of Mathematics and Information Sciences, Tokyo Metropolitan University, Hachioji 192-0397, Japan

Received: December 31, 2016

Revised: June 30, 2017

Published: September 2017

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Abstract

Chen, Kung and Morita [5] studied a variational problem corresponding to the FitzHugh-Nagumo type reaction-diffusion system (FHN type RD system), and they proved the existence of a heteroclinic solution to the system.

Motivated by [5], we consider a variational problem corresponding to FHN type RD system which involves heterogeneity. We prove the existence of a heteroclinic solution to the problem under certain conditions on the heterogeneity. Moreover, we give some information about the location of the transitions.

Keywords:

Variational problem,
FitzHugh-Nagumo type reaction diffusion systems,
heteroclinic solution.

Mathematics Subject Classification: Primary: 35J50, 35K57; Secondary: 35Q92.

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