关键词: 非线性方程组, 奇摄动, 初值问题, 渐近解, 初始层

Abstract: The authors studied singularly perturbed initial value problem for a class of system of nonlinear equations. According to the problem, the corresponding solution is expanded as the series form with small parameterε. With the aid of the corrective method of initial layer, the approximate of outer solution and corre ctive terms of initial layer are constructed successively. Uniformly valid asymptotic solutions of the problemand their asymptotic behavior are obtained.

Key words: system of nonlinear equations, singular perturbation, initial value problem, asymptotic solution, initial layer