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论文类型：期刊论文

发表时间：2016-04-15

发表刊物：JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

收录刊物：SCIE、ESI高被引论文

卷号：436

期号：2

页面范围：970-982

ISSN号：0022-247X

关键字：Chemotaxis; Global existence; Large time behavior; Logistic source; Convergence rate

摘要：We study the global attractors to the chemotaxis system with logistic source: u(t) - Delta u + chi del . (u del v) = au - bu(2), Tvt - Delta v = -v + u in Omega x R+, subject to the homogeneous Neumann boundary conditions, where smooth bounded domain Omega subset of R-N, with chi, b > 0, a is an element of R, and tau is an element of {0,1}. For the parabolic elliptic case with tau = 0 and N > 3, we obtain that the positive constant equilibrium (a/b, a/b) is a global attractor if a > 0 and b > max{N-2/N chi, chi root a/4}. Under the assumption N = 3, it is proved that for either the parabolic elliptic case with tau = 0, a > 0, b > max{chi/3,chi root a/4}, or the parabolic parabolic case with tau = 1, a > 0, b > chi root a/4 large enough, the system admits the positive constant equilibrium (a/b, a/b) as a global attractor, while the trivial equilibrium (0, 0) is a global attractor if a <= 0 and b > 0. It is pointed out that here the convergence rates are established for all of them. The results of the paper mainly rely on parabolic regularity theory and Lyapunov functionals carefully constructed. (C) 2015 Published by Elsevier Inc.