# American Institute of Mathematical Sciences

January  2012, 17(1): 417-428. doi: 10.3934/dcdsb.2012.17.417

## Traveling wave solutions in an integro-differential competition model

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

Received  June 2010 Revised  April 2011 Published  October 2011

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.
Citation: Liang Zhang, Bingtuan Li. Traveling wave solutions in an integro-differential competition model. Discrete & Continuous Dynamical Systems - B, 2012, 17 (1) : 417-428. doi: 10.3934/dcdsb.2012.17.417
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