The Cauchy problem for a singularly perturbed integro-differential Fredholm equation

被引：14
|
作者：
Nefedov N.N. [1 ]
Nikitin A.G. [1 ]
机构：
[1] Faculty of Physics, Moscow State University, Leninskie gory, Moscow
来源：
Computational Mathematics and Mathematical Physics | 2007年 / 47卷 / 4期
基金：
俄罗斯基础研究基金会;
关键词：
Asymptotic technique; Cauchy problem; Method of upper and lower solutions; Singularly perturbed integro-differential Fredholm equation;
D O I：
10.1134/S0965542507040082
中图分类号：
学科分类号：
摘要：
An initial problem is considered for an ordinary singularly perturbed integro-differential equation with a nonlinear integral Fredholm operator. The case when the reduced equation has a smooth solution is investigated, and the solution to the reduced equation with a corner point is analyzed. The asymptotics of the solution to the Cauchy problem is constructed by the method of boundary functions. The asymptotics is validated by the asymptotic method of differential inequalities developed for a new class of problems. © Nauka/Interperiodica 2007.
引用
收藏
页码：629 / 637
页数：8
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