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Indexed by:期刊论文

Date of Publication:2016-04-15

Journal:JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Included Journals:SCIE、ESI高被引论文

Volume:436

Issue:2

Page Number:970-982

ISSN No.:0022-247X

Key Words:Chemotaxis; Global existence; Large time behavior; Logistic source; Convergence rate

Abstract: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.