一类非线性奇摄动Dirichlet边值问题的匹配解法

The Matching Method for a Class of Dirichlet Boundary Value Problems of Nonlinear Singular Perturbation

利用匹配渐近展开法,讨论一类形如εy″+(xn-k)(y′+ym)=0的非线性奇摄动方程的Dirichlet边值问题,并且通过对参数k的五种不同取值的分类探讨,得到了该问题必有左边界层、右边界层或内部层之一的结论(其中左、右边界层又各分为两种类型).进而给出该问题解的零次渐近展开式,推广并改进了已有的结果.

A class of Dirichlet boundary value problems of nonlinear singularly perturbed equation,εy″＋（x″-k）（y′-y″）=0, is discussed with the matching asymptotic expanding method. According to the five different value of the parameter, It can be drawn out that, the problem must have one of the boundary layer at left, right or interior （either the left or the right boundary layer has two different types）. The zero order asymptotic expansions of the problems are also given, and the result known is improved and generalized.