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

作　　者：李五明[1] 

机构地区：[1]河南理工大学数学与信息科学学院,河南焦作454000

出　　处：《河南理工大学学报（自然科学版）》2012年第2期235-238,共4页Journal of Henan Polytechnic University（Natural Science）

基　　金：国家自然科学基金资助项目(11071057);河南理工大学青年基金资助项目(Q2011-15)

摘　　要：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.

关 键 词：特征线方法 一阶偏微分方程 解析解 

分 类 号：O175.22[理学—数学]