Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Traveling waves for a diffusive Lotka-Volterra competition model I: singular perturbations

Pages: 79 - 95, Volume 3, Issue 1, February 2003      doi:10.3934/dcdsb.2003.3.79

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Yuzo Hosono - Department of Information and Communication Sciences, Kyoto Sangyo University, Kyoto 603-8555, Japan (email)

Abstract: This paper concerns traveling wave solutions for a two species competition-diffusion model with the Lotka-Volterra type interaction. We assume that the corresponding kinetic system has only one stable steady state that one of species is existing and the other is extinct, and that the rate $\epsilon_{2}$ of diffusion coefficients of the former species over the latter is small enough. By singular perturbations, we prove the existence of traveling waves for each $c \ge c(\epsilon)$ and discuss the minimal wave speed.

Keywords:  Traveling wave, Lotka-Volterra model, competition, minimal wave speed.
Mathematics Subject Classification:  35K57, 34E20, 92D2.

Received: January 2001;      Revised: June 2002;      Available Online: November 2002.