# American Institute of Mathematical Sciences

February  2003, 3(1): 79-95. doi: 10.3934/dcdsb.2003.3.79

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

 1 Department of Information and Communication Sciences, Kyoto Sangyo University, Kyoto 603-8555, Japan

Received  January 2001 Revised  June 2002 Published  November 2002

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.
Citation: Yuzo Hosono. Traveling waves for a diffusive Lotka-Volterra competition model I: singular perturbations. Discrete & Continuous Dynamical Systems - B, 2003, 3 (1) : 79-95. doi: 10.3934/dcdsb.2003.3.79
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