Existence of travelling waves with their minimal speed for a diffusing Lotka-Volterra system

Authors:
Ning Fei;Jack Carr
Affiliations:
Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, UK;Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, UK
Venue:
Nonlinear Analysis: Real World Applications
Year:
2003

Citing 2
Cited 1

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Nonlinear Analysis: Theory, Methods & Applications
Fisher wave fronts for the Lotka-Volterra competition model with diffusion

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Travelling wave and global attractivity in a competition-diffusion system with nonlocal delays

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Abstract

Travelling waves are natural phenomena ubiquitously for 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 wave-- with its minimal speed.