Critical mass for an attraction-repulsion chemotaxis system.

This paper determines the critical mass for the attraction-repulsion chemotaxis system: <inline-graphic></inline-graphic>, <inline-graphic></inline-graphic>, <inline-graphic></inline-graphic>, subject to the non-flux boundary condition in a bounded domain <inline-graphic></inline-graphic> with <inline-graphic></inline-graphic>, <inline-graphic></inline-graphic>. It was known that the solutions are globally bounded if <inline-graphic></inline-graphic>. In this paper, we prove with <inline-graphic></inline-graphic> that the solutions must be globally bounded whenever the initial mass <inline-graphic></inline-graphic>, and the finite time blow-up may occur if <inline-graphic></inline-graphic>. [ABSTRACT FROM AUTHOR]