The sub-supersolution method for the FitzHugh-Nagumo type reaction-diffusion system with heterogeneity

Takashi Kajiwara

doi:10.3934/dcds.2018101

Article Contents

2018, Volume 38, Issue 5: 2441-2465. Doi: 10.3934/dcds.2018101

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The sub-supersolution method for the FitzHugh-Nagumo type reaction-diffusion system with heterogeneity

Takashi Kajiwara

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

Received: July 31, 2017

Published: June 2018

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Abstract

We construct a heteroclinic solution to the FitzHugh-Nagumo type reaction-diffusion system (FHN RD system) with heterogeneity by the sub-supersolution method due to [5]. $σ(d,γ)$ is introduced as the Rayleigh quotient corresponding to a linearized eigenvalue problem of the subsolution, where $d$ and $γ$ are parameters. The key to construct the solution is the uniform estimate for $σ(·,·)$ from below. In addition, it enables us to analyze an asymptotic behavior of the solution.

Keywords:

Sub-supersolution method,
FitzHugh-Nagumo type reaction diffusion systems,
heteroclinic solution.

Mathematics Subject Classification: Primary: 34C37, 35K57; Secondary: 35J50.

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References

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