| 张映辉,谭忠,孙明保.一个耦合双曲-抛物系统的全局光滑解[J].数学年刊A辑,2013,34(1):29~46 |
| 一个耦合双曲-抛物系统的全局光滑解 |
| Global Smooth Solutions to a Coupled Hyperbolic-Parabolic System |
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| DOI： |
| 中文关键词: 全局光滑解,双曲-抛物系统,趋化,凸熵 |
| 英文关键词:Global smooth solution, Hyperbolic-parabolic system, Chemotaxis,Convex entropy |
| 基金项目:国家自然科学基金(No.11226170, No.11271305, No.11271128), 中国博士后科学基金(No.2012M511640), 湖南省教育厅研究基金(No.11C0628, No.11A043), 湖南理工学院基金(No.2011Y49),湖南省重点建设学科项目 |
| Author Name | Affiliation | E-mail | | ZHANG Yinghui | The Hubei Key Laboratory of Mathematical Physics, School of Mathematics
and Statistics, Central China Normal University, Wuhan 430079, China
School
of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006,
Hunan, China. | zhangyinghui1009@yahoo.com.cn | | TAN Zhong | School of Mathematical Sciences, Xiamen University, Xiamen 361005, Fujian,
China. | ztan85@163.com | | SUN Mingbao | School of Mathematics, Hunan Institute of Science and Technology, Yueyang
414006, Hunan, China. | sun_mingbao@163.com |
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| 中文摘要: |
| 考虑一个源自生物学的耦合双曲-抛物模型的初边值问题. 当动能函数为非线性函数以及初始值具有小的$L^2$能量但其$H^2$能量可能任意大时, 得到了初边值问题光滑解的全局存在性和指数稳定性. 而且, 如果假定非线性动能函数满足一定的条件, 在对初值没任何小条件假定下得到光滑解的全局存在性. 通过构造一个新的非负凸熵和做精细的能量估计得到了结果的证明. |
| 英文摘要: |
| The authors investigate the initial-boundary value problem for a coupled hyperbolic-parabolic system arising from biology. When the kinetic function is nonlinear and the initial data are of small $L^2$-norm energy but possibly large $H^2$-norm energy, the authors get both the global existence and the exponential stability of smooth solutions to the initial-boundary value problem. Furthermore, assuming that the nonlinear kinetic function satisfies certain conditions, the authors establish the global existence of smooth solutions without any smallness assumption on the initial data. The proof is obtained by constructing a new nonnegative convex entropy and making delicate energy estimates. |
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