Uniqueness of traveling front solutions for the Lotka-Volterra system in the weak competition case

Yang Wang; Xiong Li

doi:10.3934/dcdsb.2018300

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2019, Volume 24, Issue 7: 3067-3075. Doi: 10.3934/dcdsb.2018300

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Uniqueness of traveling front solutions for the Lotka-Volterra system in the weak competition case

Yang Wang^1, and
Xiong Li^2, ,

1.
School of Mathematical Sciences, Shanxi University, Taiyuan, 030006, China
2.
School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

* Corresponding author: Xiong Li
* Corresponding author: Xiong Li

Received: March 2018

Revised: July 2018

Early access: October 2018

Published: May 2019

The second author is supported by NSF grant 11571041 and the Fundamental Research Funds for the Central Universities.

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Abstract

In this paper, we will prove the uniqueness of traveling front solutions with critical and noncritical speeds, connecting the origin and the positive equilibrium, for the classical competitive Lotka-Volterra system with diffusion in the weak competition, which partially answers the open problem presented by Tang and Fife in [17]. In fact, once these traveling front solutions have the same wave speed and the same asymptotic behavior at $ξ = ±∞$, they are unique up to translation.

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Mathematics Subject Classification: Primary: 35C07, 35K57; Secondary: 92D25.

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References

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