高维波动方程的间接解法  

Indirect method of high-dimensions wave equation

作　　者：师夏阳[1] 丁宣浩[1] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《商丘师范学院学报》2009年第3期23-27,共5页Journal of Shangqiu Normal University

基　　金：国家自然科学基金资助项目(No.10361003);广西自然科学基金资助项目(No.0640165);广西区研究生创新计划资助项目(No.2007105950701M04)

摘　　要：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.

关 键 词：波动方程 热传导方程 间接方法 

分 类 号：O175.8[理学—数学]