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

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

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