This paper deals with nonnegative solutions of a fully parabolic two-species chemotaxis system with competitive kinetics under homogeneous Neumann boundary conditions in a N-dimensional bounded smooth domain with reasonably smooth nonnegative initial data. In a previous paper of Bai & Winkler (2016), the equilibrium of the global bounded classical solution was shown in both coexistence and extinction cases. We extend this result to weak solutions and prove these solutions globally exist and finally converge to the same semi-trivial steady state in a certain sense.

中文翻译：

---

具有后勤来源的两种种群趋化系统的渐近性

本文在具有合理光滑非负初始数据的N维有界光滑域中，研究了均质Neumann边界条件下具有竞争动力学的完全抛物型两族趋化系统的非负解。在Bai＆Winkler（2016）的先前论文中，在共存和灭绝案例中都显示了整体有界经典解的平衡。我们将此结果推广到弱解，并证明这些解在全球范围内存在，并最终在一定意义上收敛到相同的半平凡稳态。