四阶椭圆型方程奇异摄动问题的渐近解  

Asymptotic Solution of Singular Perturbation Problems for the Fourth-Order Elliptic Differential Equations

作　　者：苏煜城[1] 刘国庆[1] 

机构地区：[1]南京大学

出　　处：《应用数学和力学》1990年第7期597-610,共14页Applied Mathematics and Mechanics

摘　　要：本文考虑了四阶椭圆型偏微分方程奇异摄动边值问题,建立了解及其导数的能量估计,并用Lyuternik-Vishik方法构造了形式渐近解.最后利用能量估计我们得到了渐近展开式余项的界.In this paper we consider the singularly perturbed boundary value problem for the fourth-order elliptic differential equation, establish the energy estimates of the solution and its derivatives and construct the formal asymptotic solution by Lyuternik-Vishik's method. Finally, by means of the energy estimates we obtain the bound of the remainder of the asymptotic solution.

关 键 词：椭圆型方程 奇异摄动问题 渐近解 

分 类 号：O175.25[理学—数学]