Georg Hetzer, Lourdes Tello
This article concerns the effect of slow diffusion in two-species competition-diffusion problem with spatially homogeneous nearly identical reaction terms. In this case all (nonnegative) equilibria are spatially homogeneous, and the set of nontrivial equilibria is the graph of a -curve. This article shows convergence of positive solutions to an equilibria which is determined by the initial data. The proof relies on the existence of a Lyapunov function and is adapted from  which dealt with linear diffusion.
Published November 20, 2015.
Math Subject Classifications: 35K57, 35K65.
Key Words: Two-species competition-diffusion system; slow dispersal; identical species; convergence to equilibria.
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| Georg Hetzer |
Department of Mathematics and Statistics
Auburn, AL 36849, USA
| Lourdes Tello |
Department of Applied Mathematics
ETS Arquitectura, Universidad Politécnica de Madrid
28040 Madrid, Spain
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