Roles of logistic source in a singular chemotaxis urban crime model
Abstract
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.
Related
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BibTeX
@misc{li2026roles,
title = {{Roles of logistic source in a singular chemotaxis urban crime model}},
author = {Bin Li and Tian Xiang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25896},
eprint = {2609.25896},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25896},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Roles of logistic source in a singular chemotaxis urban crime model
AU - Bin Li
AU - Tian Xiang
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.25896
UR - https://arxiv.org/abs/2609.25896
AB - 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.
ER -