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Indexed by:期刊论文

Date of Publication:2016-06-01

Journal:DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B

Included Journals:SCIE

Volume:21

Issue:4

Page Number:1317-1327

ISSN No.:1531-3492

Key Words:Chemotaxis; Keller-Segel system; boundedness; nonlinear sensitivity

Abstract: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).