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一类带反应项的Othmer-Stevens型趋化模型解的存在性 被引量：2

Existence of Solution to Some Othmer-Stevens Chemotaxis System with Reaction Term
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摘要 该文讨论了一类带反应项的Othmer-Stevens型趋化模型的初边值问题证明了:如果边界θΩ∈C^(2+β),函数Φ(x,t,w),f(x,t,u)和g(x,t,u,w)充分光滑,则该系统存在唯一解. In this paper, the authors study an initial-boundary value problem of Othmer-Stevens chemotaxis system with reaction term in the master equation {δu/δt=D∨（u ∨ln u/Φ（x, t, w））＋ f（x, t, u）, δw/δt=g（x, t, u, w）, u∨ln u/Φ（x, t, w） δn→=0. They prove that there exists a unique solution if the boundary δΩ ∈C2＋β, the functions Φ（x, t, w）, f（x, t, u） and g（x, t, u, w） are sufficiently smooth.
作者 李俊锋 刘伟安
机构地区 武汉大学数学与统计学院
出处 《数学物理学报（A辑）》 CSCD 北大核心 2009年第6期1561-1571,共11页 Acta Mathematica Scientia
基金 国家自然科学基金(10471108)资助
关键词 趋化 Othmer—Stevens模型 紧算子 不动点. Chemotaxis Othmer-Stevens model Compact operator Fixed point
分类号 O175.15 [理学—基础数学] TQ028.8 [化学工程]
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参考文献18

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同被引文献20

  • 1Howard A. Levine,Brian D. Sleeman,Marit Nilsen-Hamilton.Mathematical modeling of the onset of capillary formation initiating angiogenesis[J]. Journal of Mathematical Biology . 2001 (3)
  • 2Levine H A,,Sleeman B D.A system of reaction diffusion equations arising in the theory of reinforced random walks. SIAM Journal on Applied Mathematics . 1997
  • 3Hillen T,Stevens A.Hyperbolic models for chemotaxis in 1-D. Nonl Anal Real World Appl . 2001
  • 4Nagai T.Global existence and blow-up of solutions to a chemotaxis system. Nonlinear Analysis . 2001
  • 5Erban R,Othmer H G.From individual to collective behavior in bacterial chemotaxis. SIAM Journal on Applied Mathematics . 2004
  • 6Senba, T,Suzuki, T.Local and norm behavior of blow up solutions to a parabolic system of chemotaxis. J. Korean Math. Soc . 2000
  • 7T. Nagai.Behavior of solutions to a parabolic-elliptic system modelling chemotaxis. J. Korean. Math. Soc . 2000
  • 8Nagai T,Senba T,Yoshida K.Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis. Funkcialaj Ekvacioj Serio Internacia . 1997
  • 9Yang Y,Chen H,Liu W A.On existence of global solutions and blow-up to a system of reaction-diffusion equations modelling chemotaxis. SIAM Journal on Mathematical Analysis . 2001
  • 10Horstmann,D.From 1970 until now: The Keller–Segel model in chemotaxis and its consequences I. Jahresber. DMV . 2003

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数学物理学报（A辑）
2009年 第6期

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