This paper is devoted to investigate the global boundedness of a two-species predator–prey chemotaxis model with one signal. By establishing the uniform boundedness of $L^2$-norm for prey and predator densities and the uniform boundedness of $L^4$-norm for the signal gradient, we consider the global existence and boundedness of classical solutions to the model in a three-dimensional bounded domain.

中文翻译：

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具有两种种群的捕食者－猎物趋化性模型的全局有界性

本文致力于研究具有一个信号的两种种群的捕食者－猎物趋化性模型的整体有界性。通过建立一致的有界性${\mathrm{大号}}^2$-捕食和被捕食者的密度的范数以及 ${\mathrm{大号}}^4$对于信号梯度，我们考虑了三维有界域中模型经典解的整体存在性和有界性。