具奇异敏感的趋向性犯罪模型中的警察威慑效应  

The Effects of Police Deployment in a Chemotaxis System with Singular Sensitivity for Criminal Activities

作　　者：李彬 谢莉 Li Bin;Xie Li(School of Statistics and Data Science,Ningbo University of Technology,Zhejiang Ningbo 315211;School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331)

机构地区：[1]宁波工程学院统计与数据科学学院,浙江宁波315211 [2]重庆师范大学数学科学学院,重庆401331

出　　处：《数学物理学报(A辑)》2025年第2期512-533,共22页Acta Mathematica Scientia

基　　金：宁波市自然基金(2022J147);重庆市科委项目(CSTB2023NSCQ-MSX0411);重庆市教委科研项目(KJZDM202000502,CXQT21014)。

摘　　要：该文在有界光滑域Ω■R^(n)(n≥3)上研究了一个带奇异灵敏度的两组分非局部模型,该模型是三组分的Jones-Brantingham-Chayes趋向性模型的一个简化模型,后者被用于模拟在警察威慑下犯罪活动的时空动态.该文在较大趋化敏感系数范围内证明了相应初边值问题拥有全局经典解.值得指出的是,相较于无警察威慑效应的Short et al趋向性犯罪模型的相关结果,警察威慑扩大了确保解全局存在的趋化敏感系数范围,在某种意义下这也表明了警察威慑效应对模型解性质具有正则化效应.注意,先前数值结果(Jones,Brantingham and Chayes.Math Models Methods Appl Sci,2010)表明警察威慑有益于镇压犯罪热点的形成,因此该文的研究结果也是相应数值结果的一个理论支持.As a simplified version of a three-component chemotaxis system introduced by Jones et al to model the spatio-temporal behavior of criminal activities under the effects of police deployment,a twocomponent non-local system with singular sensitivity is considered over a bounded domain Ω■R^(n) with n≥3.For all reasonably regular initial data,the existence of classical solution of the corresponding initial-boundary value problem is established globally in time.In particular,we enlarge the range of chemotactic sensitivity Xi,compared to known results on the Short et al model which describes the spatio-temporal behavior of criminal activities without the effects of police deployment,which reveals that the police deployment has a regularization effect on solution.This is also a theoretical supplement to the previously numerical result unveiled by Jones,Brantingham and Chayes(Math Models Methods Appl Sci,2010)that the police deployment is beneficial for suppressing the formation of criminal hotspots.

关 键 词：趋向性模型 奇异敏感 经典解 全局存在性 长时间行为 

分 类 号：O175.2[理学—数学]