ON THE PERIODIC SOLUTION OF THE KELLER-SEGEL MODEL OF CHEMOTAXIS WITH A LOGISTIC SOURCE

The paper investigates a system of three parabolic equations, which is a model of the spatiotemporal state of two competing populations of species, both of which are chemotactically attracted by the same signal substance. Individuals move according to random diffusion and chemotaxis, and both populations reproduce themselves and mutually compete with each other according to the classical Lotka-Volterra kinetics. The global existence and uniqueness of the classical solutions of this system is proved by the contraction mapping principle using a priori Lp estimates and Schauder-type estimates for parabolic equations.

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