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

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.