Georg Hetzer, Tung Nguyen, Wenxian Shen
Abstract:
Of concern is the effect of a small spatially inhomogeneous
perturbation of the reproduction rate of the first species in a
two-species Lotka-Volterra competition-diffusion problem with
spatially homogeneous reaction terms. Apart from this perturbation
and the diffusion rates, the two species are assumed to be identical.
Our main result shows that the first species can always invade,
whereas the second species can only invade under certain conditions
which yield uniform persistence of both species. The proof relies on
comparison techniques and properties of the principal eigenvalue
of reaction-diffusion equations.
Submitted December 9, 2009. Published November 5, 2010.
Math Subject Classifications: 35K57
Key Words: Lotka-Volterra two-species competition-diffusion system;
nearly identical species; invasion; uniform persistence.
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Georg Hetzer Department of Mathematics and Statistics Auburn University Auburn, AL 36849, USA email: hetzege@auburn.edu |
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Tung Nguyen Department of Mathematical Sciences University of Illinois at Springfield Springfield, IL 62703, USA email: tnguy2@uis.edu |
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Wenxian Shen Department of Mathematics and Statistics Auburn University Auburn, AL 36849, USA email: wenxish@auburn.edu |
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