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Indexed by:期刊论文

Date of Publication:2019-12-01

Journal:NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS

Included Journals:SCIE、EI

Volume:50

Page Number:532-561

ISSN No.:1468-1218

Key Words:Chemotaxis; Singular sensitivity; Signal absorption; Logistic source

Abstract:In this paper we study the non-flux chemotaxis system: u(t) = Delta u - chi del.(u/v del v) + bu - mu u(2), v(t) = Delta v - uv, in a bounded and smooth domain Omega subset of R-2, with b is an element of R and chi, mu > 0. The existing literature, on the premise of relatively weak cross-diffusion with 0 < chi < 1, has established the global existence of classical solutions for arbitrary mu > 0. In the present paper, we extend to prove that for any chi >= 1, there exists mu(*)(chi) > 0 such that whenever mu > mu(*)(chi), any reasonably smooth initial data emanates a unique global classical solution. Moreover, it is shown that there exist alpha(Omega) > 0 and beta(Omega) > 0 such that when b > 0, if mu > alpha(Omega)b + beta(Omega) for 0 < chi < 1, or mu > max{mu(*)(chi), alpha(Omega)b +beta(Omega)} for chi >= 1, then any classical solution must be globally bounded with the convergence that (u(. , t), vertical bar del v(., t)vertical bar/v(. ,t), v(. , t)) -> (b/mu , 0, 0) in [L-infinity(Omega)](3) as t -> infinity. Instead, when b <= 0, all classical solutions remain uniformly bounded in time as long as mu > 0 for 0 < chi < 1, or mu > mu(*)(chi) for chi >= 1, and it also holds that (u(. , t), vertical bar del v(. , t)vertical bar/v(. ,t) ,v(. , t)) -> (0, 0, lambda) in [L-infinity(Omega)](3) as t -> infinity with 0 <= lambda < 1/vertical bar Omega vertical bar integral(Omega) v(. , 0). (C) 2019 Elsevier Ltd. All rights reserved.