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Indexed by:Journal Papers

Date of Publication:2015-10-01

Journal:JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Included Journals:SCIE、ESI高被引论文、Scopus

Volume:430

Issue:1

Page Number:585-591

ISSN No.:0022-247X

Key Words:Boundedness; Keller-Segel system; Chemotaxis; Global existence; Logistic source

Abstract:This paper deals with the higher dimension quasilinear parabolic-parabolic Keller-Segel system involving a source term of logistic type u(t) = del center dot (phi(u)del u) - chi del. (u del v) g(u), tau vt = Delta v - v + u in Omega x (0,T), subject to nonnegative initial data and homogeneous Neumann boundary condition, where Omega is a smooth and bounded domain in R-n, n >= 2, phi and g are smooth and positive functions satisfying ks(p) <= phi when s >= s(0) > 1, g(s) <= g(s) <= as - mu s(2) for s > 0 with g(0) >= 0 and constants a >= 0, tau, chi, mu > 0. It is known that the model without the logistic source admits both bounded and unbounded solutions, identified via the critical exponent 2/n. On the other hand, the model is just a critical case with the balance of logistic damping and aggregation effects, for which the property of solutions should be determined by the coefficients associated. In the present paper it is proved that there is theta(0) > 0 such that the problem admits global bounded classical solutions whenever chi/mu < theta(0), regardless of the size of initial data and diffusion. This shows the substantial effect of the logistic source has on the behavior of solutions. (C) 2015 Elsevier Inc. All rights reserved.