Traveling Spots on Multi-Dimensional Excitable Media

Yan Yu Chen, Hirokazu Ninomiya, Ryotaro Taguchi

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this paper, the existence of a traveling spot on multi-dimensional ex-citable media is studied. First, the equations for the front and the back of a traveling spot including the interface equation are derived from the singular limit analysis of the reaction-diffusion system of the FitzHugh-Nagumo type. Then, the existence and uniqueness for the front and the back are shown when the speed of the traveling spot is less than the one of a planar wave. In addition, the non-convexity of the traveling spots is shown depending on the speed. Finally, the traveling spot converges to the planar wave as its speed tends to the one of the planar wave, which means that a traveling spot connects a stationary solution and a planar wave.

Original languageEnglish
Pages (from-to)281-305
Number of pages25
JournalJournal of Elliptic and Parabolic Equations
Volume1
Issue number2
DOIs
Publication statusPublished - 1 Oct 2015

Keywords

  • Asymptotic
  • parabolic
  • travelling spots

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