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August, 2018 Invasion Entire Solutions for a Three Species Competition-diffusion System
Guang-Sheng Chen, Shi-Liang Wu
Taiwanese J. Math. 22(4): 859-880 (August, 2018). DOI: 10.11650/tjm/171001


The purpose of this paper is to study a three species competition model with diffusion. It is well known that there exists a family of traveling wave solutions connecting two equilibria $(0,1,1)$ and $(1,0,0)$. In this paper, we first establish the exact asymptotic behavior of the traveling wave profiles at $\pm \infty$. Then, by constructing a pair of explicit upper and lower solutions via the combination of traveling wave solutions, we derive the existence of some new entire solutions which behave as two traveling fronts moving towards each other from both sides of $x$-axis. Such entire solution provides another invasion way of the stronger species to the weak ones.


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Guang-Sheng Chen. Shi-Liang Wu. "Invasion Entire Solutions for a Three Species Competition-diffusion System." Taiwanese J. Math. 22 (4) 859 - 880, August, 2018.


Received: 29 July 2017; Revised: 8 October 2017; Accepted: 16 October 2017; Published: August, 2018
First available in Project Euclid: 26 October 2017

zbMATH: 06965400
MathSciNet: MR3830824
Digital Object Identifier: 10.11650/tjm/171001

Primary: 34K30 , 35K57 , 92D30

Keywords: competition system , existence , invasion entire solution , Traveling wave

Rights: Copyright © 2018 The Mathematical Society of the Republic of China


Vol.22 • No. 4 • August, 2018
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