论Helmholtz方程的一类边界积分方程的合理性

本文导出了Helmholtz 方程超定边值问题有解的一个充要条件,和用非解析开拓法证明了文1]中的Helmholtz 方程在外域中的解的边界积分表示式的合理性,并将此类边界积分表示式推广用于带空洞的有限域。这样就比较严密而又浅近地证明了基于该表示式建立起来的间接变量和直接变量边界积分方程的合理性。

On the Rationality of a Class of Boundary Integral Equations for Helmholtz Equation

A necessary and sufficient condition for the existence of solution of the over-determined boundary val-ue problem of Helmholtz equation is presented and the universality of the boundary integral representationfor the solution of Helmholtz equation given in1]is proved by the method of non-analytic continuation.Thus the rationality of the class of boundary integral equations with indirect and direct unknowns based onthe above mentioned representation is proved rigorously.