Quasilinear systems and residential burglary

In this talk we will present some results for systems of equations modeling residential burglary.
For the parabolic system model proposed by Andrea Bertozzi et-al, we study the equilibrium case. By using bifurcation theory we show that this system does support pattern formation. We also give some results concerning stability of the bifurcating patterns. These results correspond to a joint work with Chris Cosner and Steve Cantrel from the University of Miami.
The model has been recently modified by Pitcher giving rise to a new parabolic system of equations. We show some results for this system that contain a condition for existence of global solutions. This work corresponds to a collaboration with Philippe Souplet and Quoc Hung Phan from Paris 13.