含慢变量奇摄动非线性方程组初始层现象

Initial layer phenomena of singular perturbed nonlinear equations with slow variable

摘要: 研究含慢变量非线性方程组初值问题 :x′=g(t,x,y) ,εy"=h(t,x,y,μy′)当 ε=O(μ2 )时的初始层性质 ,通过压缩映射证明了摄动解的存在 ,得到了解的一致有效的渐近展开式

Abstract: This paper studies the property of initial layer of initial value problem for the nonlinear equations with slow variable x′=g(t,x,y),εy"=h(t,x,y,μy′) when ε=O(μ 2) By contraction mapping,the existence of perturbed solutions is proved and the uniformly valid asymptotic expansions of the solutions are obtained.