Existence Of Travelling Waves With Their Minimal Speed For A Diffusing Lotka-Volterra System

Travelling waves are natural phenomena ubiquitously reaction-diffusion systems in many scientific areas, such as in biophysics, population genetics, mathematical ecology, chemistry, chemical physics, and so on. It is pretty well understood for a diffusing Lotka-Volterra system that there exist travelling wave solutions which propagate from an equilibrium point to another one. In this paper, we prove there exists, at least, a wave front-the monotone travelling wavewith its minimal speed. (C) 2003 Elsevier Science Ltd. All rights reserved.