Global solutions to a higher‐dimensional system related to crime modeling

We consider the systemu t = Δ u − χ ∇ ·u v ∇ v − u v + B 1v t = Δ v − v + u v + B 2of partial differential equations for some positive χ and some Ω ⊂ R n , n  ≥ 2. While there are results regarding the existence of global solutions in one dimension for any χ  > 0, there are not yet any for the higher‐dimensional case. This work in which we establish global solutions for any χ ∈ 0 , 2 nis a first step toward filling this gap.