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论文类型：期刊论文

发表时间：2016-06-01

发表刊物：DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B

收录刊物：SCIE

卷号：21

期号：4

页面范围：1317-1327

ISSN号：1531-3492

关键字：Chemotaxis; Keller-Segel system; boundedness; nonlinear sensitivity

摘要：This paper considers the parabolic-parabolic Keller-Segel system with nonlinear sensitivity u(t) = Delta u - del(u(alpha)del v), v(t) = Delta v - v+u, subject to homogeneous Neumann boundary conditions with smooth and bounded domain Omega subset of R-n , n >= 1. It is proved that if alpha >= max{1, 2/n}, then the solutions are globally bounded, and both the components u and v decay to the same constant steady state (u) over bar0 = 1/vertical bar Omega vertical bar integral(Omega) u(0)(x)dx exponentially in the L-infinity-norm provided both parallel to u(0)parallel to L-q*((Omega)) and parallel to del v(0)parallel to(Lp)* ((Omega)) small enough with q* = n alpha K/n+K, p* = n alpha K/n+K-n alpha, K is an element of [n, 2n alpha - n] boolean AND ((alpha - 1)n, infinity).