一个广义双曲抛物系统的全局光滑解的存在性和指数稳定性  

Existence and Exponential Stability of Global Smooth Solutions to a Generalized Hyperbolic-Parabolic System

作　　者：张映辉[1] 邓海英[2] 潘晓[3] 

机构地区：[1]湖南理工学院数学学院,湖南岳阳414006 [2]湖南第一师范学院,长沙410002 [3]湖南理工学院南湖学院,湖南岳阳414006

出　　处：《湖南理工学院学报（自然科学版）》2011年第3期9-11,47,共4页Journal of Hunan Institute of Science and Technology(Natural Sciences)

基　　金：湖南省教育厅项目(11C0628);湖南理工学院科研项目(2011Y49)

摘　　要：考虑一个双曲抛物系统的初边值问题,当动能函数为非线性函数且初始值的H^2范数任意大时,得到了全局光滑解的存在性和指数稳定性.这些结果推广了以前相关的结果,因为以前相关的结果都是关于线性的动能函数或者初始值的H^2范数充分小的情形.The initial boundary value problem for a generalized hyperbolic-parabolic system was considered. When nonlinear kinetics and smooth initial data which have small L2 -norm energy, may have arbitrarily large H2-norm energy, existence and exponential stability of global smooth solutions were obtained. These results generalize previous related results on smooth solutions for kinetic function being linear or H2-norm of the initial data being sufficiently small.

关 键 词：双曲抛物系统 全局光滑解 存在性 指数稳定性 

分 类 号：O175.2[理学—数学]