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...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.展开更多
基金Supported by the National Natural Science Foundation of China(No.11371161)
文摘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.
