简单波的解析解

Riemann于1860年给出了简单波的一般解,可是欲将其中所含的一个任意函数的具体形式按边界条件或初始条件求出来,却难以实现,因而对具体问题就难以深入探讨.本文按拟线性偏微分方程的几何理论,十分方便地给出了由边界条件或初始条件所确定的简单波解析解,并用这些解讨论了有关流动的性质,且得到了若干新颖的结果

Analytic Solutions of Simple Waves

B. Riemann furnished the general solution of simple waves in I860"'. But it is difficult to, find out the exact forms of the arbitrary function contained in the general solution which must satisfy boundary or initial conditions.For this reason it is inconvenient to probe into the character ristics of concrete problems. In this paper the analytic solutions of simple waves are afforded according to the geometric theory of quassi-linear partial differential equations, and they are determined with boundary or initial conditions. By using Lhese solutions the specific properties of certain flows are discussed and novel results are obtained.