发表机构
Ningbo University of Technology; Renmin University of China（宁波工程学院; 中国人民大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文系统研究了逻辑斯蒂源在奇异趋化城市犯罪模型中的作用，发现强阻尼确保经典解有界收敛并防止犯罪热点，弱阻尼确保广义解全局存在且最终光滑收敛，显著改进扩展了先前结果。
AI 中文摘要
本文系统地展示了逻辑斯蒂源在奇异趋化城市犯罪模型中对经典解的全局有界性和收敛性，以及广义解的全局存在性、最终光滑性和收敛性的作用。粗略地说，这项工作表明，适当（可以精确）强的逻辑斯蒂阻尼确保经典解的有界性和收敛性，而弱的逻辑斯蒂阻尼确保广义解的全局存在性及其最终光滑性以及在二维和三维中的收敛性。前者特别意味着强逻辑斯蒂阻尼可以防止犯罪热点（空间模式）的形成。因此，先前在此方面的已知结果得到了显著改进和扩展。
英文摘要
In this paper, we systematically exhibit the roles of logistic source on global boundedness and convergence of classical solutions, and global existence and eventual smoothness as well as convergence of generalized solutions for a singular chemotaxis urban crime model. Roughly speaking, this work shows that suitably (can be precise) strong logistic damping ensures boundedness and convergence of classical solutions, and weak logistic damping ensures global existence of generalized solution and its eventual smoothness as well as convergence in two and three dimensions. The former in particular implies that strong logistic damping can prevent the formation of crime hotspots (spatial patterns). Previous known results in this respect are thus significantly improved and extended.
CommentsThe first version was submitted to a journal on August 19, 2026. 43 pages
