初值为零的高维波动方程的解

The solution of undulatory equation of higher dimension whose initial value is zero

对于n =1,2 ,3的波动方程的柯西问题 ,可以利用分离变量法和 ,降维法 ,给出其满足初始条件的求解公式 ,但当n >3时 ,在利用Fourier变换求解过程中 ,会遇到发散的广义积分 .文中给出了n维Fourier变换、性质及其逆变换 ,利用阶跃函数的Fourier变换 ,δ -函数的性质 ,给出了高维波动方程的求解公式。

Canchy problem of undulation equation to n=1,2,3, given out solution's formula with satisfied initial condition, using separate variable way and low dimension way but when you will meet emission generalized integral, during use Fourier change solution. This article gives out the change of n dimension Fourier , its character and converse change . It uses δ- function and unit bound function and shows the explanation of undulatory equation of higher dimension which more than 3.