矩形域上具有转向线的二阶线性椭圆方程的边值问题  

A Class of Elliptic Equation Boundary Value Problems with a Turning Line on the Rectangle Region

作　　者：魏雪蕊[1] 包立平[2] 

机构地区：[1]绍兴文理学院数学系,绍兴312000 [2]杭州电子科技大学理学院,杭州310018

出　　处：《工程数学学报》2012年第1期107-111,共5页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10871226);绍兴文理学院重点资助项目[010LG1001]~~

摘　　要：在矩形域上研究了一类具有转向线的奇摄动二阶线性椭圆方程的边值问题.在坐标变换的基础上,利用分离变量法和匹配法,得到了一类二阶线性非齐次常微分方程.通过分析奇摄动常微分方程产生共振的充分条件和必要条件,确定了二阶线性椭圆方程边值问题解的渐近性态.We discuss a class of boundary value problems of the singular perturbation elliptic equations with a turning line on a rectangle region. On the basis of coordinate transformation, the second-order nonhomogeneous ordinary dierential equations are obtained by using methods of separation of variables and matching asymptotic expansions. Through considering the suffcient and necessary conditions at resonance for the singular perturbation ordinary differential equations, the asymptotic behaviors of the solutions for the boundary value problems of two-order elliptic equations are also evaluated.

关 键 词：奇异摄动 转向线 共振 渐近性态 

分 类 号：O175.25[理学—数学]