一类非齐次波动方程Cauchy问题的求解

The Solving of the Cauchy Problem of Non-homogeneous Wave Equation

研究一类自由项为f(x,t)=(c1t+c2).g(x)的波动方程Cauchy问题的求解问题.通过简单的变量变换,可将这类问题归化为自由振动的Cauchy问题,从而可用D′Alembert公式求解,省去了计算推迟势这项复杂的二重积分,使问题的求解变得简单快捷有效.

The solving of Cauchy problem of the wave equation with free term is studied. By the simple variable change, the problem be converted to Cauchy problem in free vibration which may be solved by D＇Alembert formulas. The method simplified the computation of the retarded potential by variable change. The examples showed that the method is fast and effective.