LOCAL EXISTENCE AND UNIQUENESS OF SOLUTIONS TO A PDE MODEL FOR CRIMINAL BEHAVIOR
NANCY RODRIGUEZ, ANDREA BERTOZZI
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Source: Crossref
Published: Sep 1, 2010
DOI: 10.1142/s0218202510004696
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The analysis of criminal behavior with mathematical tools is a fairly new idea, but one which can be used to obtain insight on the dynamics of crime. In a recent work, 34 Short et al. developed an agent-based stochastic model for the dynamics of residential burglaries. This model produces the right qualitative behavior, that is, the existence of spatio-temporal collections of criminal activities or "hotspots", which have been observed in residential burglary data. In this paper, we prove local existence and uniqueness of solutions to the continuum version of this model, a coupled system of partial differential equations, as well as a continuation argument. Furthermore, we compare this PDE model with a generalized version of the Keller–Segel model for chemotaxis as a first step to understanding possible conditions for global existence versus blow-up of the solutions in finite time.
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