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.

中文翻译：

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具有种内和种间竞争的两种出租车系统解的有界有界性。

在本文中，我们研究了一个非线性的反应扩散方程组，该方程组由一个与完全抛物线趋化系统耦合的普通方程组成。该系统为争夺共同资源的两个种群的进化构成了数学模型，其中一个种群具有趋化性。在适当的假设下，我们在二维有界域中证明了该系统在时间上的全局存在性和经典解的有界性。此外，针对问题数据的特定情况，获得了解决方案的渐近行为。