特征线方法及其在求解偏微分方程中的应用

Characteristic method and its some applications in solving partial differential equations

针对一阶线性双曲型偏微分方程,要求其Cauchy问题的解析解,提出特征线方法 .特征线方法的基本思想是将偏微分方程的Cauchy问题转化为常微分方程的相应问题,通过解常微分方程进而得到原来偏微分方程问题的解.通过对特征线方法的研究,得到了求解一阶线性双曲型偏微分方程Cauchy问题解的一般步骤,同时给出了一些应用.

For one order linear hyperbolic partial differential equation , we aim to obtain the analytic solution of the Cauehy problem, so we propose characteristic method. The fundamental idea is to transform the Cauchy problem of partial differential equation into the corresponding problem of order differential equation. By solving the order differential equation, we can obtain the solution of the former partial differential equation. Through studying method of characteristics, we get the general steps of solving the Cauehy problem of one order linear hyperbolic partial differential equation. Furthermore, we give some applications.