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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
*
[email protected]
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Abstract

Many models in biology and ecology can be described by reaction-diffusionequations wit time delay. One of important solutions for these type of equationsis the traveling wave solution that shows the phenomenon of wave propagation.The existence of traveling wave fronts has been proved for large class ofequations, in particular, the monotone systems, such as the cooperativesystems and some competition systems. However, the problem on the uniqueness oftraveling wave (for a fixed wave speed) remains unsolved. In this paper, we showthat, 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 wavesmonotonesystems
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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