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论文类型：期刊论文

发表时间：2015-10-01

发表刊物：JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

收录刊物：SCIE、ESI高被引论文、Scopus

卷号：430

期号：1

页面范围：585-591

ISSN号：0022-247X

关键字：Boundedness; Keller-Segel system; Chemotaxis; Global existence; Logistic source

摘要：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.