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Uniqueness of Monotone Mono-stable Waves forReaction-Diffusion Equations with Time Delay

Published online by Cambridge University Press:  26 March 2009

W. Huang ,
M. Han  and
M. Puckett
W. Huang*
Affiliation:
Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899, USA
M. Han
Affiliation:
Department of Mathematics, Sanghai Normal University Shangai, China
M. Puckett
Affiliation:
Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899, USA
*
huang@math.uah.edu
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Abstract

Many models in biology and ecology can be described by reaction-diffusion equations wit time delay. One of important solutions for these type of equations is the traveling wave solution that shows the phenomenon of wave propagation. The existence of traveling wave fronts has been proved for large class of equations, in particular, the monotone systems, such as the cooperative systems and some competition systems. However, the problem on the uniqueness of traveling wave (for a fixed wave speed) remains unsolved. In this paper, we show that, for a class of monotone diffusion systems with time delayed reaction term, the mono-stable traveling wave font is unique whenever it exists.

Keywords

reaction-diffusion equationstime delaytraveling wavesmonotone systems
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 4 , Issue 2: Delay equations in biology , 2009 , pp. 48 - 67
Copyright
© EDP Sciences, 2009

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