Standing Pulse Solutions for the FitzHugh-Nagumo Equations

Yoshihito Oshita, Isamu Ohnishi

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We are basically concerned with existence of standing pulse solutions for an elliptic equation with a nonlocal term. The problem comes from an activator-inhibitor system such as the FitzHugh-Nagumo equations with inhibitor's diffusion or arises in the Allen-Cahn equation with the nonlocal term. We prove it mathematically rigorously in a bounded domain Ω ⊂ Rn (n ≥ 2) with smooth boundary, by employing the Lyapunov-Schmidt reduction method, which is the same kind of way as used typically in [2], [9], [10], [13], for instance.

Original languageEnglish
Pages (from-to)101-115
Number of pages15
JournalJapan Journal of Industrial and Applied Mathematics
Volume20
Issue number1
DOIs
Publication statusPublished - Feb 2003
Externally publishedYes

Keywords

  • Standing pulse solutions
  • The FitzHugh-Nagumo equations

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

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