Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2016-11-01

Journal: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Included Journals: Scopus、SCIE

Volume: 443

Issue: 1

Page Number: 445-452

ISSN: 0022-247X

Key Words: Keller-Segel system; Chemotaxis; Singular sensitivity; Boundedness

Abstract: We consider a parabolic-parabolic Keller-Segel system of chemotaxis model with singular sensitivity: u(t) = Delta u-chi del.(u/v del v), v(t) = k Delta v - v+u under the homogeneous Neumann boundary condition in a smooth bounded domain Omega subset of R-n (n >= 2), with chi, k > 0. It is proved that for any k > 0, the problem admits global classical solutions, whenever chi is an element of (0,-k-1/2 +1/2 root(k - 1)(2) + 8k/n). The global solutions are moreover globally bounded if n <= 8. This shows a way the size of the diffusion constant k of the chemicals v affects the behavior of solutions. (c) 2016 Elsevier Inc. All rights reserved.