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Communications on Pure and Applied Analysis (CPAA)
 

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

Pages: 131 - 150, Volume 16, Issue 1, January 2017      doi:10.3934/cpaa.2017006

 
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Kun Li - College of Science, National University of Defense Technology, Changsha, 410073, China (email)
Jianhua Huang - Department of Mathematics, National University of Defense Technology, Changsha, 410073, China (email)
Xiong Li - Department of Mathematical Sciences, Beijing Normal University, Beijing 100875, China (email)

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.

Received: January 2016;      Revised: August 2016;      Available Online: November 2016.

 References