| Issue |
Math. Model. Nat. Phenom.
Volume 4, Number 2, 2009
Delay equations in biology
|
|
|---|---|---|
| Page(s) | 48 - 67 | |
| DOI | https://doi.org/10.1051/mmnp/20094203 | |
| Published online | 26 March 2009 | |
Uniqueness of Monotone Mono-stable Waves for Reaction-Diffusion Equations with Time Delay
1
Department of Mathematical Sciences, University of Alabama in
Huntsville, Huntsville, AL 35899, USA
2
Department of Mathematics, Sanghai Normal University
Shangai, China
Corresponding author: huang@math.uah.edu
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.
Mathematics Subject Classification: 34K99 / 35K57 / 92B99
Key words: reaction-diffusion equations / time delay / traveling waves / monotone systems
© EDP Sciences, 2009
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