Unboundedness phenomenon in a model of urban crime
Unboundedness phenomenon in a model of urban crime
We show that spatial patterns ("hotspots") may form in the crime model \begin{equation} \left\{\; \begin{aligned} u_{t} &= \tfrac{1}{\varepsilon}\Delta u - \tfrac{\chi}{\varepsilon} \nabla \cdot \left(\tfrac{u}{v} \nabla v \right) - \varepsilon uv, \\ v_{t} &= \Delta v - v + u v, \end{aligned} \right. \end{equation} which we consider in $\Omega = B_R(0) …