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

  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},
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
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