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

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  • 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.

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


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