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

Abstract

This paper concerns traveling wave solutions for a two speciescompetition-diffusion model with the Lotka-Volterra typeinteraction. We assume that the corresponding kinetic system hasonly one stable steady state that one of species is existing and theother is extinct, and that the rate $\epsilon_{2}$ of diffusioncoefficients of the former species over the latter is small enough.By singular perturbations, we prove the existence of traveling wavesfor each $c \ge c(\epsilon)$ and discuss the minimal wave speed.