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Indexed by:期刊论文

Date of Publication:2014-10-01

Journal:MATHEMATICAL METHODS IN THE APPLIED SCIENCES

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

Volume:37

Issue:15

Page Number:2326-2330

ISSN No.:0170-4214

Key Words:quasilinear parabolic equations; cell movement (chemotaxis); Keller-Segel system; chemotaxis; global existence; logistic source

Abstract:We study a quasilinear parabolic-elliptic Keller-Segel system involving a source term of logistic type u(t)=delta(phi(u)delta u)-delta(u delta v)+g(u),-v=-v+u in x(0,T), subject to nonnegative initial data and the homogeneous Neumann boundary condition in a bounded domain < subset of>Rn with smooth boundary, n1, >0, phi c(1)s(p) for ss(0)>1, and g(s)as-s(2) for s>0 with a,g(0)0, >0. There are three nonlinear mechanisms included in the chemotaxis model: the nonlinear diffusion, aggregation and logistic absorption. The interaction among the triple nonlinearities shows that together with the nonlinear diffusion, the logistic absorption will dominate the aggregation such that the unique classical solution of the system has to be global in time and bounded, regardless of the initial data, whenever , required by globally bounded solutions of the quasilinear K-S system without the logistic source. Copyright (c) 2013 John Wiley & Sons, Ltd.