This paper is concerned with a ratio-dependent predator-prey system with diffusion and cross- diffusion in a bounded domain with no flux boundary condition. We show that under certain hypotheses, the cross-diffusion c...This paper is concerned with a ratio-dependent predator-prey system with diffusion and cross- diffusion in a bounded domain with no flux boundary condition. We show that under certain hypotheses, the cross-diffusion can create non-constant positive steady states even though the corresponding model without cross-diffusion fails.展开更多
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 in part by the National Natural Science Foundation of China under Grant No.11601542 and 11626238
文摘This paper is concerned with a ratio-dependent predator-prey system with diffusion and cross- diffusion in a bounded domain with no flux boundary condition. We show that under certain hypotheses, the cross-diffusion can create non-constant positive steady states even though the corresponding model without cross-diffusion fails.
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.
