Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2018-08-01

Journal: NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS

Included Journals: Scopus、EI、SCIE

Volume: 42

Page Number: 120-139

ISSN: 1468-1218

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

Abstract: We consider a chemotaxis consumption system with singular sensitivity and logistic source: u(t) = Delta u - del . (u phi(v)del v) + ru - mu u(k), v(t) = Delta v - uv in a smooth bounded domain Omega subset of R-n (n >= 1), where r, mu > 0, k > 1, and phi(s) is an element of C-1(0, infinity) satisfying phi(s) -> infinity as s -> 0. It is proved that there exists a global classical solution if k > 1 for n = 1 or k > 1 + n/2 for n >= 2. The asymptotic behavior of solutions is determined as well for phi(v) = 1/v, n = 2 that if k > 2, there exists mu(*) > 0 such that (u, v, vertical bar del u vertical bar/v) -> ((r/mu)(1/k-1),0,0) as t infinity provided mu > mu(*). (C) 2017 Elsevier Ltd. All rights reserved.