# American Institute of Mathematical Sciences

September  2013, 12(5): 2083-2090. doi: 10.3934/cpaa.2013.12.2083

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

 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  March 2012 Revised  September 2012 Published  January 2013

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.
Citation: Jong-Shenq Guo, Ying-Chih Lin. The sign of the wave speed for the Lotka-Volterra competition-diffusion system. Communications on Pure & Applied Analysis, 2013, 12 (5) : 2083-2090. doi: 10.3934/cpaa.2013.12.2083
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