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A system of reaction-diffusion equations modeling two-species competition in an unstirred che- mostat is considered. The asymptotic behavior of solutions is given as a function of the parameters, and it is determined when neither, one, or both competing populations survive. Techniques include the maximum principle, theory of uniform persistence in infinite-dimensional dynamical systems, and the theory of strongly order-preserving semidynamical system.

On a System of Reaction-Diffusion Equations Arising from Competition in an Unstirred Chemostat