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November  2017, 16(6): 2133-2156. doi: 10.3934/cpaa.2017106

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

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

Received  January 2017 Revised  July 2017 Published  July 2017

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.

Citation: Takashi Kajiwara. A Heteroclinic Solution to a Variational Problem Corresponding to FitzHugh-Nagumo type Reaction-Diffusion System with Heterogeneity. Communications on Pure & Applied Analysis, 2017, 16 (6) : 2133-2156. doi: 10.3934/cpaa.2017106
##### References:

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##### References:
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