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On the structure of steady solutions for the kinematic model of spiral waves in excitable media

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Abstract

Spiral waves are commonly observed in biological and chemical systems. Representing each wave front by a single curve, Brazhnik, Davydov, and Mikhailov introduce a kinematic model equation. The aim of this paper is to provide a detailed analysis for the steady state solutions of these equations. The existence of asymptotically Archimedean solutions is analytically shown.

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Authors and Affiliations

  1. Graduate School of Mathematical Sciences, University of Tokyo, Komaba, 153-8914, Tokyo, Japan

    Ryo Ikota

  2. Department of Mathematics, Hitotsubashi University, Kunitachi, 186-8601, Tokyo, Japan

    Naoyuki Ishimura

  3. National Institute of Materials and Chemical Research, Higashi 1-1, Tsukuba, 305-8565, Ibaraki, Japan

    Tomohiko Yamaguchi

Authors
  1. Ryo Ikota
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  2. Naoyuki Ishimura
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  3. Tomohiko Yamaguchi
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Dedicated to Professor Seiji Ukai on his sixtieth birthday.

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Ikota, R., Ishimura, N. & Yamaguchi, T. On the structure of steady solutions for the kinematic model of spiral waves in excitable media. Japan J. Indust. Appl. Math. 15, 317 (1998). https://doi.org/10.1007/BF03167407

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  • DOI: https://doi.org/10.1007/BF03167407

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