边界和算子双摄动的高阶椭圆型方程一般边值问题解的渐近式

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Asymptotic Expression of the Solution of General Boundary Value Problem for Higher Order Elliptic Equation with Perturbation Both in Boundary and in Operator

摘要: 本文在文[1]和[2]的基础上研究边界和算子双摄动的高阶椭圆型方程一般边值问题的奇摄动,建立含两参数的渐近解表达式,导出求渐近解的迭代过程,给出余项估计,改进和拓广了前文的工作.

Abstract: In this paper basing on [1] and [2], we study the singular perturbation of general boundary value problem for higher order elliptic equation with perturbation both in the boundary and in the operator, so as to establish the asymptotic expression involving two parameters. Thus, the iterative process of finding the asymptotic solution is derived and the estimation of the remainder term is given out, we extend and improve the previously published papers.

[1]	林宗池,四阶椭圆型方程在一股边界条件下的奇摄动,福建师大学报(自然科学版).1(1980),1-8.
[2]	林宗池,在一般边界条件下高阶椭圆型方程的奇摄动,福建师大学报,(自然科学版),2(1980),1-12.
[3]	Lions,J.L,and Magenes,E.,Non-I;omo eneous Boundary Value Problem and Applications,Springer-Verlag,New York,Heideberg,Berlin,(1972).
[4]	BesJes,J,G.,Singular perfurbation problem for linear elliptic differential operators of arbitrary order,J.Math.Annal.and Appl.,49(1975),24-46.
[5]	江福汝、高汝熹,高阶椭圆型方程一般边夜问题的奇摄动,科学通报,23(1979).1057-1061.