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Global solutions to a higher‐dimensional system related to crime modeling
Author(s) -
Freitag Marcel
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5141
Subject(s) - mathematics , dimension (graph theory) , partial differential equation , work (physics) , mathematical analysis , pure mathematics , thermodynamics , physics
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.