Traveling Wave Solutions in a Reaction-Diffusion Model for Criminal Activity

@article{Berestycki2013TravelingWS,
  title={Traveling Wave Solutions in a Reaction-Diffusion Model for Criminal Activity},
  author={Henri Berestycki and Nancy Rodr{\'i}guez and Lenya Ryzhik},
  journal={Multiscale Modeling & Simulation},
  year={2013},
  volume={11},
  pages={1097-1126}
}
We study a reaction-diffusion system of partial differential equations, which can be taken to be a basic model for criminal activity, first introduced in [3]. We show that the assumption of a populations natural tendency towards crime significantly changes the long-time behavior of criminal activity patterns. Under the right assumptions on these natural tendencies we first show that there exists traveling wave solutions connecting zones with no criminal activity and zones with high criminal… CONTINUE READING
Highly Cited
This paper has 45 citations. REVIEW CITATIONS

From This Paper

Figures, tables, and topics from this paper.

Explore Further: Topics Discussed in This Paper

References

Publications referenced by this paper.
Showing 1-10 of 21 references

A statistical model of criminal

M. B. Short, M. R. D’Orsogna, +4 authors L. B. Chayes
behavior. Math. Models Methods Appl. Sci., • 2008
View 4 Excerpts
Highly Influenced

Wave-Block in Excitable Media Due to Regions of Depressed Excitability

SIAM Journal of Applied Mathematics • 2000
View 5 Excerpts
Highly Influenced

Mohler and Martin B . Short . Geographic profiling from kinetic models of criminal behavior

O. George
SIAM Journal of Applied Mathematics • 2012

Entire solutions of reaction-diffusion equations and an application to discrete diffusive equations

Jong-Shenq Guo, Yoshihisa Morita
Discrete Contin. Dyn. Syst., • 2005
View 2 Excerpts

Existence, uniqueness and bounds for a problem in combustion theory

Mohammed Al-Refai
J. Comput. Appl. Math., • 2004
View 1 Excerpt