Abstract
In this paper we study a nonlinear system of reaction–diffusion differential equations consisting of an ordinary equation coupled to a fully parabolic chemotaxis system. This system constitutes a mathematical model for the evolution of two populations that are competing for a common resource, one of which is subject to chemotaxis. Under suitable assumptions we prove the global in time existence and the boundedness of the classical solutions of this system in a two-dimensional bounded domain. In addition, the asymptotic behavior of the solutions for a particular case of the problem data is obtained.
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