半空间上双曲—抛物方程大初值问题的的全局分析  

Global Analysis of Hyperbolic-Parabolic Equations with Large Initial Data on Half Space

作　　者：张映辉[1] 潘晓[1] 

机构地区：[1]湖南理工学院,湖南岳阳414006

出　　处：《湖南理工学院学报（自然科学版）》2014年第1期8-11,共4页Journal of Hunan Institute of Science and Technology(Natural Sciences)

基　　金：国家自然科学基金项目(11301172;11226170);湖南理工学院教改项目(2013B09)

摘　　要：建立了半空间上双曲—抛物系统大初值问题光滑解的全局存在性和渐近行为.跟以前相关的结果相比,他们都要求各种小初始条件假设,我们能够证明半空间上双曲—抛物系统任意大初值问题光滑解的整体存在性和渐近行为.对此的证明是基于构造一个非负凸熵和做精细的能量估计.We establish existence and asymptotic behavior of global smooth solutions to the half space problem for a hyperbolic-parabolic system with large initial data. Compared to the previous related results, where various smallness conditions on initial data were proposed, we are able to prove global existence and asymptotic behavior of smooth solutions to the half space problem for a hyperbolic-parabolic system with arbitrarily large initial data. The proof is based on constructing nonnegative convex entropy and making delicate energy estimates.

关 键 词：双曲-抛物系统 全局光滑解 存在性 渐近行为 

分 类 号：O175.2[理学—数学]