Boundedness in a fully parabolic quasilinear repulsion chemotaxis model of higher dimension
Boundedness in a fully parabolic quasilinear repulsion chemotaxis model of higher dimension
复制标题
高维全抛物线拟线性排斥趋化模型中的有界性
DOI：
10.1007/s11766-020-3994-5
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发表时间：
2020-06
期刊：
影响因子：
--
通讯作者：
杨金戈
中科院分区：
文献类型：
--
作者：
周双双;宫婷;杨金戈
We deal with the boundedness of solutions to a class of fully parabolic quasilinear repulsion Chemotaxis systems \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{cases}u_{t}= \nabla \cdot(\phi(u)\nabla{u})+\nabla\cdot(\psi(u)\nabla{v}), & (x,t)\in\Omega\times(0,T),\\v_{t}=\Delta{v}-v+u, & (x,t)\in\Omega\times(0,T),\end{cases}$$\end{document} under homogeneous Neumann boundary conditions in a smooth bounded domain Ω ⊂ ℝN(N≥ 3), where 0 <ψ(u) ≤K(u+ 1)α,K1(s+ 1)m≤ϕ(s) ≤K2(s+ 1)mwithα, K, K1,K2> 0 andm∈ ℝ. It is shown that if, then for any sufficiently smooth initial data, the classical solutions to the system are uniformly-in-time bounded. This extends the known result for the corresponding model with linear diffusion.
We deal with the boundedness of solutions to a class of fully parabolic quasilinear repulsion Chemotaxis systems \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{cases}u_{t}= \nabla \cdot(\phi(u)\nabla{u})+\nabla\cdot(\psi(u)\nabla{v}), & (x,t)\in\Omega\times(0,T),\\v_{t}=\Delta{v}-v+u, & (x,t)\in\Omega\times(0,T),\end{cases}$$\end{document} under homogeneous Neumann boundary conditions in a smooth bounded domain Ω ⊂ ℝN(N≥ 3), where 0 <ψ(u) ≤K(u+ 1)α,K1(s+ 1)m≤ϕ(s) ≤K2(s+ 1)mwithα, K, K1,K2> 0 andm∈ ℝ. It is shown that if, then for any sufficiently smooth initial data, the classical solutions to the system are uniformly-in-time bounded. This extends the known result for the corresponding model with linear diffusion.
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DOI：
10.1137/100802943
发表时间：
2011-03
期刊：
SIAM J. Math. Anal.
影响因子：
--
作者：
Youshan Tao;M. Winkler
通讯作者：
Youshan Tao;M. Winkler
DOI：
10.3934/dcdsb.2013.18.2705
发表时间：
2013-10
影响因子：
1.2
作者：
Youshan Tao
通讯作者：
Youshan Tao
DOI：
10.4064/bc81-0-7
发表时间：
2008
期刊：
Banach Center Publications
影响因子：
--
作者：
Tomasz Cieślak;P. Laurençot;C. Morales-Rodrigo
通讯作者：
Tomasz Cieślak;P. Laurençot;C. Morales-Rodrigo
DOI：
10.1007/s00033-015-0532-z
发表时间：
2015-04
期刊：
Zeitschrift für angewandte Mathematik und Physik
影响因子：
--
作者：
Qingshan Zhang;Yuxiang Li
通讯作者：
Qingshan Zhang;Yuxiang Li
影响因子：
1.9
作者：
Hillen, T.;Painter, K. J.
通讯作者：
Painter, K. J.