Coexistence and extinction in the Volterra-Lotka competition model with nonlocal dispersal

Georg Hetzer; Tung Nguyen; Wenxian Shen

doi:10.3934/cpaa.2012.11.1699

Article Contents

2012, Volume 11, Issue 5: 1699-1722. Doi: 10.3934/cpaa.2012.11.1699

This issue Previous Article A class of large amplitude oscillating solutions for three dimensional Euler equations Next Article Generalized and weighted Strichartz estimates

Coexistence and extinction in the Volterra-Lotka competition model with nonlocal dispersal

1.
Department of Mathematics, Auburn University, AL 36849-5310
2.
Department of Mathematical Sciences, University of Illinois Springeld, Springeld, IL 62703
3.
Department of Mathematics and Statistics, Auburn University, Auburn University, AL 36849-5310

Received: January 2011

Revised: June 2011

Published: September 2012

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Abstract

Coexistence and extinction for two species Volterra-Lotka competition systems with nonlocal dispersal are investigated in this paper. Sufficient conditions in terms of diffusion, reproduction, self-limitation, and competition rates are established for existence, uniqueness, and stability of coexistence states as well as for the extinction of one species. The focus is on environments with hostile surroundings. In this case, our results correspond to those for random dispersal under Dirichlet boundary conditions. Similar results hold for environments with non-flux boundary and for periodic environments, which correspond to those for random dispersal under Neumann boundary conditions and periodic boundary conditions, respectively.

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Mathematics Subject Classification: 35K55, 47G20, 47N20, 92D25, 92D40.

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