退化方程具有重根的奇摄动初值问题解的渐近分析

Asymptotic Analysis for the Singularly Perturbed Initial Value Problem with Degenerate Equation Having Multiple Root

摘要: 本文研究退化方程具有重根的奇摄动一阶非线性微分方程初值问题的渐近解的构造。为了获得更为精细的边界层刻画，本文采用修正的边界层函数法，得到具有指数衰减渐近特性的边界层函数。利用所获得的形式渐近解去构造上下解，证得该形式渐近解的一致有效性。

Abstract: In this paper, the asymptotic behavior of the initial value problem for the singularly perturbed first order nonlinear differential equation with a degenerate equation having roots of multiplicity two is studied. With the purpose of obtaining a more precise description of the boundary layer, the modified method of boundary layer function is applied to construct the boundary layer function possessing the behavior of exponential decay characteristic and then the asymptotic solution is constructed and used to prove that the formal asymptotic solution is uniformly valid.