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一个模拟趋化现象的广义双曲-抛物系统的光滑解的全局分析
引用本文:张映辉,谭 忠,赖柏顺,孙明保.一个模拟趋化现象的广义双曲-抛物系统的光滑解的全局分析[J].数学年刊A辑(中文版),2012,33(1):27-38.
作者姓名:张映辉  谭 忠  赖柏顺  孙明保
作者单位:湖南理工学院数学学院;厦门大学数学科学学院;河南大学现代数学研究所
基金项目:国家自然科学基金(No.10976026,No.10871061);湖南省教育厅基金(No.11C0628);湖南理工学院基金(No.2011Y49)资助的项目
摘    要:考虑一个模拟趋化现象的广义双曲-抛物系统的Cauchy问题,当动能函数为非线性函数且初始值具有小的L~2能量但其H~2能量可能任意大时,得到了全局光滑解的存在性和渐近行为.这些结果推广了以前的关于动能函数为线性函数或初始值具有小的H~2能量情形下的相关结果,首次获得了关于全局光滑大解方面的结果.这些结果的证明基于构造一个新的非负凸熵和做精细的能量估计.

关 键 词:全局分析  双曲-抛物系统  趋化  凸熵

Global Analysis of Smooth Solutions to a Generalized Hyperbolic-Parabolic System Modeling Chemotaxis
ZHANG Yinghui;TAN Zhong;LAI Baishun;SUN Mingbao.Global Analysis of Smooth Solutions to a Generalized Hyperbolic-Parabolic System Modeling Chemotaxis[J].Chinese Annals of Mathematics,2012,33(1):27-38.
Authors:ZHANG Yinghui;TAN Zhong;LAI Baishun;SUN Mingbao
Institution:1 School of Mathematics,Hunan Institute of Science and Technology,Yueyang 414006,Hunan,China. 2 School of Mathematical Sciences,Xiamen University,Xiamen 361005,Fujian, China. 3 Institute of Contemporary Mathematics,Henan University,Kaifeng 475004, Henan,China.
Abstract:The authors establish the existence and the asymptotic behavior of global smooth solutions to the Cauchy problem for a generalized hyperbolic-parabolic system modeling chemotaxis with the nonlinear kinetic function and smooth initial data which have small L~2-norm energy,but possibly large H~2-norm energy.These results generalize previous related results on smooth solutions for the kinetic function being linear or H~2-norm of the initial data being sufficiently small,and are first obtained for global smooth solutions with arbitrarily large H~2-norm.The proof is based on constructing a new nonnegative convex entropy and making delicate energy estimates.
Keywords:Global analysis  Hyperbolic-parabolic system  Chemotaxis  Convex entropy
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