Global well‐posedness and uniform boundedness of a higher dimensional crime model with a logistic source term

Abstract

We study a class of reaction–advection–diffusion system for χ > 0 in a smooth bounded domain with n ≥ 2. In comparison with original urban crime models (Short et al., 2008), the system introduces the logistic source term u − u2 + β to represent the fierce competition among criminals, which helps to reduce difficulties brought by the nonlinear growth term uv and large advection rate. We prove that, for n ≥ 2, suppose then the classical solutions (u, v) of the above system are uniformly bounded for any χ > 0. Our result expands χ to be arbitrary positive number.