Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2018-01-01

Journal: APPLICABLE ANALYSIS

Included Journals: Scopus、SCIE

Volume: 97

Issue: 13

Page Number: 2349-2354

ISSN: 0003-6811

Key Words: Chemotaxis; Keller-Segel system; attraction-repulsion; boundedness; blow-up

Abstract: This paper determines the critical mass for the attraction-repulsion chemotaxis system: ut = Delta u-chi del center dot (u. v)+ center dot (u. w), 0 = Delta v+ alpha u - beta v, 0 = Delta w +. u -dw, subject to the non-flux boundary condition in a bounded domain Delta R2 with.,. = 0, a, ss,., d > 0. It was known that the solutions are globally bounded if.a -.. < 0. In this paper, we prove with.a -.. > 0 that the solutions must be globally bounded whenever the initial mass integral(Omega)u0(x)dx > 4/chi alpha-xi gamma., and the finite time blow-up may occur if integral(Omega)u0(x)dx > 4/chi alpha-xi gamma.