2014 Madrid Conference on Applied Mathematics in honor of Alfonso Casal,
Electron. J. Diff. Eqns., Conference 22 (2015), pp. 47-51.

A convergence theorem for a two-species competition system with slow diffusion

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 $C^1$-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: Two-species competition-diffusion 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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