一类奇摄动双曲型非线性积分-微分系统

冯依虎; 莫嘉琪

doi:10.3969/j.issn.1000-5641.2017.03.004

一类奇摄动双曲型非线性积分-微分系统

doi: 10.3969/j.issn.1000-5641.2017.03.004

冯依虎^1,,
莫嘉琪²

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

基金项目:

国家自然科学基金 11202106

安徽省教育厅自然科学重点基金 KJ2015A347

安徽省教育厅自然科学重点基金 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

详细信息

作者简介:
冯依虎, 男, 硕士, 副教授, 研究方向为应用数学.E-mail：fengyihubzsz@163.com

中图分类号: O175.29
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- 被引次数: 0
出版历程
- 收稿日期: 2016-03-17
- 刊出日期: 2017-05-25

A class of singularly perturbed hyperbolic nonlinear integral-differential system

FENG Yi-hu^1
,,
MO Jia-qi²

1.
Department of Electronics and Information Engineering, Bozhou College, Bozhou Anhui 236800, China
2.
Department of Mathematics, Anhui Normal University, Wuhu Anhui 241003, China

摘要

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.
- 积分-微分方程 /
- 奇摄动 /
- 双曲型方程
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.
- integral-differential equation /
- singular perturbation /
- hyperbolic type equation

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参考文献(17)

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