We consider an initial-boundary value problem describing the formation of colony patterns of bacteria Escherichia coli. This model consists of reaction-diffusion equations coupled with the Keller-Segel system from the chemotaxis theory in a bounded domain, supplemented with zero-flux boundary conditions and with non-negative initial data. We answer questions on the global in time existence of solutions as well as on their large time behaviour. Moreover, we show that solutions of a related model may blow up in a finite time.

中文翻译：

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趋化性大肠杆菌菌落 PDE 模型的数学处理

我们考虑描述细菌大肠杆菌菌落模式形成的初始边界值问题。该模型由反应扩散方程与有界域中趋化性理论中的 Keller-Segel 系统相结合，并辅以零通量边界条件和非负初始数据。我们回答有关解决方案的全局时间存在以及它们的大时间行为的问题。此外，我们表明相关模型的解决方案可能会在有限的时间内爆炸。