Traveling waves of a Lotka-Volterra strong competition system with nonlocal dispersal

Guo-Bao Zhang; Ruyun Ma; Xue-Shi Li

doi:10.3934/dcdsb.2018035

Article Contents

2018, Volume 23, Issue 2: 587-608. Doi: 10.3934/dcdsb.2018035

This issue Previous Article High order Gauss-Seidel schemes for charged particle dynamics Next Article Stability of travelling waves in a Wolbachia invasion

Traveling waves of a Lotka-Volterra strong competition system with nonlocal dispersal

1.
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, China
2.
School of Mathematics, Lanzhou City University, Lanzhou, Gansu 730070, China

Author Bio: E-mail address:mary@nwnu.edu.cn (R. Ma); E-mail address:lixueshi0925@126.com(X.-S. Li)
E-mail address:zhanggb2011@nwnu.edu.cn(G.-B. Zhang)
E-mail address:zhanggb2011@nwnu.edu.cn(G.-B. Zhang)

Received: March 31, 2016

Revised: June 30, 2017

Early access: November 2017

Published: June 2018

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Abstract

This paper is concerned with the traveling waves of a nonlocal dispersal Lotka-Volterra strong competition model with bistable nonlinearity. We first establish the asymptotic behavior of traveling waves at infinity. Then by applying the stronger comparison principle and the sliding method, we prove that the traveling waves with nonzero speed are strictly monotone. Moreover, the uniqueness of wave speeds is also obtained.

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Mathematics Subject Classification: Primary: 35K57, 34K60; Secondary: 92D25.

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