2014 Madrid Conference on Applied Mathematics in honor of Alfonso Casal,
Electron. J. Diff. Eqns., Conference 22 (2015), pp. 4751.
A convergence theorem for a twospecies competition system with
slow diffusion
Georg Hetzer, Lourdes Tello
Abstract:
This article concerns the effect of slow diffusion in
twospecies competitiondiffusion 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 [6] which dealt with linear
diffusion.
Published November 20, 2015.
Math Subject Classifications: 35K57, 35K65.
Key Words: Twospecies competitiondiffusion system; slow dispersal;
identical species; convergence to equilibria.
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Georg Hetzer
Department of Mathematics and Statistics
Auburn University
Auburn, AL 36849, USA
email: hetzege@auburn.edu


Lourdes Tello
Department of Applied Mathematics
ETS Arquitectura, Universidad Politécnica de Madrid
28040 Madrid, Spain
email: l.tello@upm.es

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