A Heteroclinic Solution to a Variational Problem Corresponding to FitzHugh-Nagumo type Reaction-Diffusion System with Heterogeneity
Takashi Kajiwara · Communications on Pure & Applied Analysis · 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.