Critical mass for an attraction–repulsion chemotaxis system

ABSTRACT

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

KEYWORDS:

• Chemotaxis
• Keller–Segel system
• attraction–repulsion
• boundedness
• blow-up

AMS SUBJECT CLASSIFICATIONS:

• 35K55
• 35B35
• 35B40
• 92C17

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11171048].