具有边界层和角层现象的半线性边值问题的渐近解

Asymptotic Solution of the Semilinear Boundary Value Problem with Phenomena of Boundary and Angular Layer

本文研究二阶半线性速值问题的奇摄动,在出现边界层和角层的现象下,导出边位问题解的n阶一致有效渐近近似式,并分别按最大模和L_2范数作出余项的估计。

In this paper we study the asymptotic solution of second order nonlinear boundary value problem, considering the phenomena of boundary and angular layer. We discuss the problem: ε2x' = g(t, x, ε), x(0, ε)=α(ε), x(1, ε) = β(ε). The n-order uniformly valid asymptotic approximation of the solution is derived and estimations of the remainder are given in maximum modulus and L2-norm, respectively.