椭圆型方程哈密顿本征解的完备性  

Completeness of eigen-solutions of elliptic PDE of Hamilton type

作　　者：钟万勰[1] 

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,辽宁大连116024

出　　处：《大连理工大学学报》2004年第1期1-6,共6页Journal of Dalian University of Technology

基　　金：国家重点基础研究发展规划项目(G1999032805);国家自然科学基金资助项目(10372019);教育部博士学科点专项科研基金资助项目(20010141024).

摘　　要：椭圆型偏微分方程导向哈密顿对偶方程而分离变量,将导致哈密顿算子矩阵的本征值问题.以端部影响函数为核的积分方程的本征解为基底,采用有限维半解析法,再导出对偶微分方程,及其Riccati代数方程,给出半无限区段的最小总势能.采用哈密顿型的本征解展开法求解之.将有限维的结果取极限,从而证明偏微分方程本征向量函数的完备性定理.The elliptic PDE is derived to Hamilton dual equation form and then the method of separation of variables is applied, which derives to eigen-problem of Hamilton dual equation. The adjoint symplectic ortho-normality relation among eigen-solutions is proved. Using the eigen-solutions of integral equation with the symmetric kernel, which is the end influence function, as the basis, the semi-analytical method is applied, for which the algebraic Riccati equation is deduced. The solution uses eigen-solutions of n-D Hamilton dual system. The minimum potential energy variational principle is used to prove the completeness theorem of the eigen-solutions.

关 键 词：哈密顿对偶体系 本征解 共轭辛正交归一 完备性 椭圆型偏微分方程 

分 类 号：O175.25[理学—数学]