偏微分方程组的一种化简方法

Way of Simplifying Partial Differential Equation Systems

以李群为工具，给出了一种化简两个自变量，两个未知函数的一阶偏微分方程组的方法．在一定的条件下，可将偏微分方程组化简为一个一阶偏微分方程．若能求出此一阶偏微分方程的解，则只需再解一个一阶常微分方程，即可得出原偏微分方程组的解．该方法可用于某些一阶偏微分方程组的求解．其中包括非定常完全气体一维均熵方程和波动方程．

By using Lie group method, a way of simplifying some first order partial differential equation systems which have two independent variables and two unknow functions is presented. Under some conditions, the partial differential equation system can be simplified to a first order partial differential equation. If the partial differential equation can be solved, then the solution of the original partial differential equation system can be obtained by solving a first order ordinary differential equation. The presented way can be used to solve some first order partial differential equation systems, including the equation of one dimentional nonsteady isentropy completed gas and the wave equation.