摘要
在n维非线性波动方程Cauchy问题的迭代解法中 ,每一个迭代步骤都需要求解一个相应的n维线性波动方程的Cauchy问题。对于n维线性波动方程Cauchy问题而言 ,只要初值适当光滑 ,其解也必适当光滑 ,且在整个半空间t≥ 0上是整体存在的。从较简单的n维线性波动方程Cauchy问题出发 ,利用球面平均法和降维法分别求出n为奇数 (n >1)和n为偶数时其解的表达式。并利用叠加原理求得了一般的n维线性齐次方程Cauchy问题和线性非齐次方程Cauchy问题的解 。
When the iterative method is applied to solve the Cauchy problem of the n -dimensional nonlinear wave equation, every iterative step is a Cauchy problem of corresponding the linear wave equation. If the initial values is adequacy smoothing, the Cauchy problem solution of the n -dimensional linear wave equation must be adequacy smoothing and exist in half space t ≥0. In this paper, first, we obtain the simpler Cauchy problem solution of the n -dimensional linear equation by using the method of spherical means and the method of the reduction dimension.Second, we obtain the general Cauchy problem solutions of the n -dimensional linear homogeneous equation and nonhomogeneous equation by using the principle of superposition. These establish a foundation for solving the Cauchy problem of the n -dimensional nonlinear wave equation.
出处
《吉林大学学报（地球科学版）》
EI
CAS
CSCD
北大核心
2002年第3期283-286,共4页
Journal of Jilin University：Earth Science Edition
基金
国土资源部"十五"重点基础项目 (2 0 0 0 10 10 2 0 4 )
关键词
非线性波动方程
线性波动方程
CAUCHY问题
球面平均法
降维法
nonlinear wave equation
linear wave equation
Cauchy problem
method of spherical means method of reduction dimension
