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Indexed by:期刊论文

Date of Publication:2016-11-01

Journal:JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Included Journals:SCIE、Scopus

Volume:443

Issue:1

Page Number:445-452

ISSN No.: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.