高维波动方程的间接解法

Indirect method of high-dimensions wave equation

给出求解高维波动方程的一种间接方法.当空间维数为奇数时,是通过适当的变换,将波动方程转化为热传导方程,利用热传导方程的结果导出所求波动方程的解;当空间维数为偶数时,是用降维法得到所求波动方程的解.这就解决了高维空间中如何求解波动方程的问题.

This paper will give a indirect method for high - dimensions wave equation , the method is adapts to high - dimensions. When space dimension n is odd, we will transform the wave equation into heat equation through appropriate transform, furthermore, we use the solution of heat equation educe the wave equation, when n is even, we can solve wave equation through deduce dimensions method. All of all, we can solve n - dimensional wave equation not only n is odd but also even.