Blow-up vs boundedness in a two-species attraction–repulsion chemotaxis system with two chemicals

Abstract

We consider the attraction–repulsion chemotaxis system in a smoothly bounded domain Ω⊆R2. When the system is parabolic–elliptic–parabolic–elliptic, we establish the finite time blow-up conditions of nonradial solutions by making a differential inequality on the moment of solutions. Apart from that, in some special cases, the solutions of the system are globally bounded without blow-up. Our results extend some known conclusions in the literature.