Blow-up,Quenching,Aggregation and Collapse in a Chemotaxis Model with Reproduction Term  

作　　者：Jun-feng LI Hua CHEN Wei-an LIU 

机构地区：[1]School of Mathematics and Statistics,Central China Normal University [2]School of Mathematics and Statistics,Wuhan University

出　　处：《Acta Mathematicae Applicatae Sinica》2014年第3期617-626,共10页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(No.11371161)

摘　　要：In this paper, we consider the following chemotaxis model with ratio-dependent logistic reactionterm{δu/δt=D △↓（△↓ u-u△↓ω/ω＋u（a-bu/w）,（x,t）∈QT,δw/δt=βu-δw,（x,t）∈ QT u△↓ln（u/w）·^→n=0, x∈δΩ,0〈t〈T,u（x,0）=u0（x）〉0,x∈^-Ω,w（x,0）=w0（x）〉0, x∈^-Ω,w（x,0）=w0（x）〉0,x∈^-ΩIt is shown that the solution to the problem exists globally if b ＋β〉 0 and will blow up or quench if b -t- ]~ 〈： 0 by means of function transformation and comparison method. Various asymptotic behavior related to different coefficients and initial data is also discussed.In this paper, we consider the following chemotaxis model with ratio-dependent logistic reactionterm{δu/δt=D △↓（△↓ u-u△↓ω/ω＋u（a-bu/w）,（x,t）∈QT,δw/δt=βu-δw,（x,t）∈ QT u△↓ln（u/w）·^→n=0, x∈δΩ,0〈t〈T,u（x,0）=u0（x）〉0,x∈^-Ω,w（x,0）=w0（x）〉0, x∈^-Ω,w（x,0）=w0（x）〉0,x∈^-ΩIt is shown that the solution to the problem exists globally if b ＋β〉 0 and will blow up or quench if b -t- ]~ 〈： 0 by means of function transformation and comparison method. Various asymptotic behavior related to different coefficients and initial data is also discussed.

关 键 词：CHEMOTAXIS ratio-dependence reproduction term blow up quench super-sub-solution 

分 类 号：O175[理学—数学]