| 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,2012,33(1):27~ |
| 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 |
| Global Analysis of Smooth Solutions to a Generalized Hyperbolic-Parabolic System Modeling Chemotaxis |
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| DOI： |
| 中文关键词: 全局分析, 双曲-抛物系统, 趋化, 凸熵 |
| 英文关键词:Global analysis, Hyperbolic-parabolic system, Chemotaxis, Convex entropy |
| 基金项目: |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| The authors establish the existence and the asymptotic behavior ofglobal smooth solutions to the Cauchy problem for a generalizedhyperbolic-parabolic system modeling chemotaxis with the nonlinearkinetic function and smooth initial data which have small $L^2$-norm energy,but possibly large $H^2$-norm energy. These results generalizeprevious related results on smooth solutions for the kinetic functionbeing linear or $H^2$-norm of the initial data being sufficientlysmall, and are first obtained for global smooth solutions witharbitrarily large $H^2$-norm. The proof is based on constructinga new nonnegative convex entropy and making delicate energyestimates. |
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