调和方程Dirichlet外问题的Green函数研究

Green Fuction of the Exterior Dirichlet Problem for Harmonic Equation

调和方程在科学实践和工程技术中有广泛的应用。在以基本解方式定义Green函数的基础上,导出了有界区域外部调和函数的积分表达式,并给出了调和方程Dirichlet外问题的Green函数及其满足的条件,最后用此Green函数给出了调和方程球域外Dirichlet问题的解。

Harmonic equation had extensive application in science and engineering.In this paper,based on the definition of Green function with basic solution,the integral expression of harmonic function in exterior of the bounded region was derived. On this basis,it gives the Green function of the exterior Dirichlet problem for harmonic equation and the conditions. Finally,by using this Green function,the solution is given in the exterior domain of a sphere,which is for the exterior Dirichlet problem of harmonic equation.