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.
出处
《大连理工大学学报》
EI
CAS
CSCD
北大核心
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).
