Invasion entire solutions in a competitionsystem with nonlocal dispersal

Wan-Tong Li; Li Zhang; Guo-Bao Zhang

doi:10.3934/dcds.2015.35.1531

Article Contents

2015, Volume 35, Issue 4: 1531-1560. Doi: 10.3934/dcds.2015.35.1531

This issue Previous Article Strong positivity of continuous supersolutions to parabolic equations with rough boundary data Next Article Spiraling bifurcation diagrams in superlinear indefinite problems

Invasion entire solutions in a competition system with nonlocal dispersal

1.
School of Mathematic and Statistics, Lanzhou University, Lanzhou, Gansu 730000
2.
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000
3.
School of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070

Received: June 30, 2013

Revised: November 30, 2013

Published: May 2017

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Abstract

This paper is concerned with invasion entire solutions of a Lotka-Volterra competition system with nonlocal dispersal, which formulate a new invasion way of the stronger species to the weaker one. We first give the asymptotic behavior of traveling wave solutions at infinity. Then by the comparison principle and sub-super solutions method, we establish the existence of invasion entire solutions which behave as two monotone waves with different speeds and coming from both sides of $x$-axis.

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Mathematics Subject Classification: Primary: 35K57, 37C65; Secondary: 92D30.

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