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

Abstract

A system of reaction-diffusion equations modeling two-species competition in an unstirred chemostat 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.