Asymptotic behavior and uniqueness of traveling wave fronts in a delayed nonlocal dispersal competitive system

Kun Li; Jianhua Huang; Xiong Li

doi:10.3934/cpaa.2017006

Article Contents

2017, Volume 16, Issue 1: 131-150. Doi: 10.3934/cpaa.2017006

This issue Previous Article A complete classification of ground-states for a coupled nonlinear Schrödinger system Next Article A comparison between random and stochastic modeling for a SIR model

Asymptotic behavior and uniqueness of traveling wave fronts in a delayed nonlocal dispersal competitive system

1.
College of Science, National University of Defense Technology, Changsha, 410073, People's Republic of China
2.
School of Mathematics and Computational Science, Hunan First Normal University, Changsha, 410205, People's Republic of China
3.
School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, People's Republic of China

Author Bio: E-mail address: kli@mail.bnu.edu.cn; E-mail address: xli@bnu.edu.cn
Jianhua Huang, E-mail address: jhhuang32@nudt.edu.cn
Jianhua Huang, E-mail address: jhhuang32@nudt.edu.cn

Received: May 31, 2016

Revised: July 31, 2016

Published: January 2018

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Abstract

This paper is concerned with the asymptotic behavior and uniqueness of traveling wave fronts connecting two half-positive equilibria in a delayed nonlocal dispersal competitive system. We first prove the existence results by applying abstract theories. And then, we show that the traveling wave fronts decay exponentially at both infinities. At last, the strict monotonicity and uniqueness of traveling wave fronts are obtained by using the sliding method in the absent of intraspecific competitive delays. Based on the uniqueness, the exact decay rate of the stronger competitor is established under certain conditions.

Keywords:

Delayed nonlocal dispersal competitive system,
traveling wave front,
asymptotic behavior,
monotonicity,
uniqueness,
upper and lower solutions.

Mathematics Subject Classification: Primary: 45G15; 35B40; 34K10.

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References

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