The sign of the wave speed for the Lotka-Volterra competition-diffusion system

Jong-Shenq Guo; Ying-Chih Lin

doi:10.3934/cpaa.2013.12.2083

Article Contents

2013, Volume 12, Issue 5: 2083-2090. Doi: 10.3934/cpaa.2013.12.2083

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The sign of the wave speed for the Lotka-Volterra competition-diffusion system

Jong-Shenq Guo^1, and
Ying-Chih Lin^2,

1.
Department of Mathematics, Tamkang University, 151, Ying-Chuan Road, Tamsui, Taipei County 25137
2.
Department of Mathematics, National Taiwan Normal University, 88, S-4, Ting Chou Road, Taipei 11677

Received: February 29, 2012

Revised: August 31, 2012

Published: August 2013

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Abstract

In this paper, we study the traveling front solutions of the Lotka-Volterra competition-diffusion system with bistable nonlinearity. It is well-known that the wave speed of traveling front is unique. Although little is known for the sign of the wave speed. In this paper, we first study the standing wave which gives some criteria when the speed is zero. Then, by the monotone dependence on parameters, we obtain some criteria about the sign of the wave speed under some parameter restrictions.

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Mathematics Subject Classification: Primary: 35K55, 35K57; Secondary: 92D25, 92D40.

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References

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