## 双曲守恒律方程的间断解

Abstract: This paper studies the characteristic line method for solving hyperbolic partial differential equations (group), of which the first-order hyperbolic equation (s) as the core research. The method of characteristics is a common method of solution of hyperbolic partial differential equations (group). By the quasi-linear partial differential equations of hyperbolic equations for the two sets of ordinary differential equations, ordinary differential equation is solved. Two groups a set of partial differential equations used to define the characteristics of line, another group used to describe changes in the solution along a given characteristic line。
Keyword： Hyperbolic equation (s)  Method of characteristics

1、绪论 ……••••1
2、线性双曲型方程（组）的特征线方法…••••2
2.1概述…••••2
2.2单个方程  …… 2
2.3双曲型方程组  • 6
2.4初边值问题  … •9
3 非线性双曲型方程（组）的特征线方法  ••11
3.1拟线性双曲守恒律方程组…… •• 11
3.2间断解……•15
3.2.1解的定义•…… 15

3.2.2Rankine-Hugoniot条件   … •16
3.2.3熵条件  ……•••16
3.2.4Riemann问题  •17
3.3非线性波（经典解情形）  ……•••17
3.3.1整体经典解  …17
3.3.2导数的突变和破裂时间18
3.3.3疏散波与压缩波18
3.4非线性波（间断解情形）… 19
3.4.1单个守恒律……•19
3.4.2激波的形成与传播……•19

1、绪论
一直以来，形如

其中

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