Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2018-09-15

Journal: MATHEMATICAL METHODS IN THE APPLIED SCIENCES

Included Journals: SCIE

Volume: 41

Issue: 13

Page Number: 4936-4942

ISSN: 0170-4214

Key Words: attraction-repulsion; boundedness; chemotaxis; logistic source; parabolic-elliptic

Abstract: In this paper, we study the attraction-repulsion chemotaxis system with logistic source: u(t) = u-delta<bold></bold>(u delta v)+delta<bold></bold>(u delta w)+f(u), 0 = v-v+u, 0 = w-w+u, subject to homogeneous Neumann boundary conditions in a bounded and smooth domain < subset of>R4, where ,,,,, and are positive constants, and f:RR is a smooth function satisfying f(s) a-bs(3/2) for all s 0 with a 0 and b > 0. It is proved that when the repulsion cancels the attraction (ie, =), for any nonnegative initial data u0C0(Omega), the solution is globally bounded. This result corresponds to the one in the classical 2-dimensional Keller-Segel model with logistic source bearing quadric growth restrictions.