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.
基金
Supported by the National Natural Science Foundation of China(No.11371161)
