Release Time:2019-03-13  Hits:

Indexed by: Journal Article

Date of Publication: 2016-04-01

Journal: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Included Journals: SCIE

Volume: 436

Issue: 1

Page Number: 382-392

ISSN: 0022-247X

Key Words: Chemotaxis; Asymptotic behavior; Logistic source; Singular sensitivity

Abstract: In this paper we study the asymptotic behavior of solutions to the parabolic-elliptic chemotaxis system with singular sensitivity and logistic source: ut = Delta u - chi del . (u/v del v) + ru - mu u(2), 0 = Delta v - v + u, subject to homogeneous Neumann boundary conditions in a bounded domain Omega subset of R-2 with smooth boundary, where chi,mu > 0 and r is an element of R. It is proved that for any nonnegative initial date u(0) is an element of C ((Omega) over bar) such that integral(Omega), u(0)(-1) < 16 mu eta vertical bar Omega vertical bar(2)/chi(2) with the constant eta relying on Omega, the solution (u(.,t),v(.,t)) converges asymptotically to the constant equilibrium (r/mu, r/mu) in the L-infinity -norm as t -> infinity if r > 2(root chi + 1 - 1)(2) + chi(2)/(16 eta vertical bar Omega vertical bar). (C) 2015 Elsevier Inc. All rights reserved.