华东师范大学学报（自然科学版） >

2017 >Issue 3: 39 - 47

DOI: https://doi.org/10.3969/j.issn.1000-5641.2017.03.004

数学

一类奇摄动双曲型非线性积分-微分系统

  • 冯依虎 ,
  • 莫嘉琪
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  • 1. 亳州学院 电子与信息工程系, 安徽 亳州 236800;
    2. 安徽师范大学 数学系, 安徽 芜湖 241003
冯依虎,男,硕士,副教授,研究方向为应用数学.E-mail：fengyihubzsz@163.com

收稿日期: 2016-03-17

  网络出版日期: 2017-05-18

基金资助

国家自然科学基金（11202106）；安徽省教育厅 自然科学重点基金（KJ2015A347，KJ2017A702）；安徽省高校优秀青年人才支持计划重点项目（gxyqZD2016520）；亳州学院科学研究项目（BSKY201431）

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A class of singularly perturbed hyperbolic nonlinear integral-differential system

  • FENG Yi-hu ,
  • MO Jia-qi
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  • 1. Department of Electronics and Information Engineering, Bozhou College, Bozhou Anhui 236800, China;
    2. Department of Mathematics, Anhui Normal University, Wuhu Anhui 241003, China

Received date: 2016-03-17

  Online published: 2017-05-18

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摘要

本文研究了一类两参数双曲型非线性积分-微分奇摄动系统.首先利用Fredholm型积分方程，得到了系统的外部解；然后用多重尺度变量方法得到了系统的边界层校正项，再利用伸长变量方法得到了系统的初始层校正项；最后由不动点理论证明了奇摄动解的合成渐近展开式的一致有效性.

关键词： 积分-微分方程; 奇摄动; 双曲型方程

本文引用格式

冯依虎 , 莫嘉琪 . 一类奇摄动双曲型非线性积分-微分系统[J]. 华东师范大学学报（自然科学版）, 2017 , (3) : 39 -47 . DOI: 10.3969/j.issn.1000-5641.2017.03.004

Abstract

A class of singularly perturbed system for the hyperbolic nonlinear integral-differential system is considered. Firstly, the outer solution to system is obtained by employing the Fredholm type integral equation. Then the boundary layer corrective term is constructed using the variables of multiple scales method. And the initial layer corrective term is found via the stretched variable method. Finally, from the fixed point theory, the uniformly valid behavior for the composed asymptotic expansion of singular perturbation solution is proved.

Key words： integral-differential equation; singular perturbation; hyperbolic type equation

参考文献

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