一类奇摄动边值问题解的套层现象

The Cover Layer Phenomenon of Solution for A Class of Singularly Perturbed Boundary Value Problems

本文揭示了一类三阶半线性方程奇摄动边值问题解的“套层”现象。利用两次伸长变量的迭代，构造了解的形式渐近展开式。再用微分不等式理论，证明了该奇摄动问题渐近解的一致有效性。

In this paper the 'cover layer' phenomenon of solution for a class of singularly perturbed boundary value problems of third order semilinear equation is revealed. Using two iterations at stretched variabler the formally asylnptotic expansion of solution is constructed. And using the theory of differential mequalities the uniformly validity of asymptotic solution for the original singularly Perturbed problems is proved.