河南理工大学学报：自然科学版
河南理工大學學報：自然科學版
하남리공대학학보：자연과학판
JOURNAL OF HENAN POLYTECHNIC UNIVERSITY
2012年
2期
235-238
,共4页
特征线方法%一阶偏微分方程%解析解
特徵線方法%一階偏微分方程%解析解
특정선방법%일계편미분방정%해석해
characteristic method%One order partial differential equations%analytic solution
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．
針對一階線性雙麯型偏微分方程，要求其Cauchy問題的解析解，提齣特徵線方法．特徵線方法的基本思想是將偏微分方程的Cauchy問題轉化為常微分方程的相應問題，通過解常微分方程進而得到原來偏微分方程問題的解．通過對特徵線方法的研究，得到瞭求解一階線性雙麯型偏微分方程Cauchy問題解的一般步驟，同時給齣瞭一些應用．
침대일계선성쌍곡형편미분방정，요구기Cauchy문제적해석해，제출특정선방법．특정선방법적기본사상시장편미분방정적Cauchy문제전화위상미분방정적상응문제，통과해상미분방정진이득도원래편미분방정문제적해．통과대특정선방법적연구，득도료구해일계선성쌍곡형편미분방정Cauchy문제해적일반보취，동시급출료일사응용．
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.
