Existence of a rotating wave pattern in a disk  for a wave front interaction model

Jong-Shenq Guo; Hirokazu Ninomiya; Chin-Chin Wu

doi:10.3934/cpaa.2013.12.1049

Article Contents

2013, Volume 12, Issue 2: 1049-1063. Doi: 10.3934/cpaa.2013.12.1049

This issue Previous Article The explicit nonlinear wave solutions of the generalized $b$-equation Next Article Travelling wave solutions of a free boundary problem for a two-species competitive model

Existence of a rotating wave pattern in a disk for a wave front interaction model

1.
Department of Mathematics, Tamkang University, 151, Ying-Chuan Road, Tamsui, Taipei County 25137
2.
Department of Mathematics, Meiji University, 1-1-1 Higashi-mita, Tama-ku, Kawasaki, 214-8571
3.
Department of Applied Mathematics, National Chung Hsing University, 250, Kuo Kuang Road, Taichung 402

Received: July 2011

Revised: November 2011

Published: March 2013

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Abstract

We study the rotating wave patterns in an excitable medium in a disk. This wave pattern is rotating along the given disk boundary with a constant angular speed. To study this pattern we use the wave front interaction model proposed by Zykov in 2007. This model is derived from the FitzHugh-Nagumo equation and it can be described by two systems of ordinary differential equations for wave front and wave back respectively. Using a delicate shooting argument with the help of the comparison principle, we derive the existence and uniqueness of rotating wave patterns for any admissible angular speed with convex front in a given disk.

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Mathematics Subject Classification: Primary: 34B15, 34B60; Secondary: 35K57.

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