关于加权残值法的充要性问题及其权函数的选择

本文论证了偏微分方程初-边值混合问题的加权残值方程的充要性条件和有关定理。关于充要性条件的讨论也为正确选择解析函数作为权函数,建立充要的加权残值方程提供了理论指导。重点讨论了边界积分方程的充要性。指出了两种满足充要条件的权函数和相应的边界积分方程。

THE PROBLEM ABOUT NECESSARY AND SUFFICIENT CONDITION FOR THE METHOD OF WEIGHTED RESIDUALS AND THE SELECTION OF WEIGHTED FUNCTIONS

In this paper, the necessary and sufficient condition for the method of weighted residuals about mixed initial-boundary value problem of partial differential equations are presented. The discussion about necessary and sufficient condition provides the theoretical foundation to select weighted functions for necessary and sufficient weighted residual aquation. We also discuss the necessary and sufficient condition for the boundary integral equation. The two kinds of weighted functions and the corresponding boundary integral equations with necessary and sufficient condition are presented.In this paper, the necessary and sufficient condition for the method of weighted residuals about mixed initial-boundary value problem of partial differential equations are presented. The discussion about necessary and sufficient condition provides the theoretical foundation to select weighted functions for necessary and sufficient weighted residual aquation. We also discuss the necessary and sufficient condition for the boundary integral equation. The two kinds of weighted functions and the corresponding boundary integral equations with necessary and sufficient condition are presented.