Self--motion of camphor discs. model and analysis

Xinfu Chen; Shin-Ichiro Ei; Masayasu Mimura

doi:10.3934/nhm.2009.4.1

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2009, Volume 4, Issue 1: 1-18. Doi: 10.3934/nhm.2009.4.1

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Self--motion of camphor discs. model and analysis

1.
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260
2.
Faculty of Mathematics, Kyushu University, Fukuoka, 812-8581
3.
Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Kawasaki, 214-8571

Received: July 2008

Revised: October 2008

Published: March 2009

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Abstract

In the present paper, a model describing the self-motion of a camphor disc on water is proposed. The stability of a standing camphor disc is investigated by analyzing the model equation, and a pitchfork type bifurcation diagram of a traveling spot is shown. Multiple camphor discs are also treated by the model equations, and the repulsive interaction of spots is discussed.

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Mathematics Subject Classification: Primary: 80A30, 58J55, 35K55, 35K57; Secondary: 93A30.

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