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

Yuzo Hosono

doi:10.3934/dcdsb.2003.3.79

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2003, Volume 3, Issue 1: 79-95. Doi: 10.3934/dcdsb.2003.3.79

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

Yuzo Hosono^1,

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

Received: December 31, 2000

Revised: May 31, 2002

Published: January 2003

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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.

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Mathematics Subject Classification: 35K57, 34E20, 92D2.

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