Traveling wave solutions in an integro-differential competition model

Liang Zhang; Bingtuan Li

doi:10.3934/dcdsb.2012.17.417

Article Contents

2012, Volume 17, Issue 1: 417-428. Doi: 10.3934/dcdsb.2012.17.417

This issue Previous Article Global stability of a five-dimensional model with immune responses and delay Next Article Blowup, global fast and slow solutions to a parabolic system with double fronts free boundary

Traveling wave solutions in an integro-differential competition model

Liang Zhang^1, and
Bingtuan Li^2,

1.
Institute of Applied Mathematics, College of Science, Northwest A & F University, Yangling, Shaanxi 712100
2.
Department of Mathematics, University of Louisville, Louisville, KY 40292

Received: June 2010

Revised: April 2011

Published: January 2012

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Abstract

We study the existence of traveling wave solutions for the two-species Lotka-Volterra competition model in the form of integro-differential equations. The model incorporates asymmetric dispersal kernels that describe long distance dispersal processes of competing species in space. Using lower and upper traveling wave solutions, we show that the model has traveling wave solutions that connect the origin and the coexistence equilibrium with speeds greater than the spreading speed of each species in the absence of its rival.

Keywords:

Mathematics Subject Classification: Primary: 92D40, 92D25, 47G20; Secondary: 34C37, 34K10.

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