中国科学技术大学学报 ›› 2020, Vol. 50 ›› Issue (2): 115-119.DOI: 10.3969/j.issn.0253-2778.2020.02.005

• 论著 • 上一篇    下一篇

一类非线性时滞奇异摄动边值问题的激波解

朱红宝,陈松林,杜亚洁   

  1. 安徽工业大学数理科学与工程学院,安徽马鞍山 243002
  • 收稿日期:2019-06-18 修回日期:2019-07-24 接受日期:2019-07-24 出版日期:2020-02-28 发布日期:2019-07-24
  • 通讯作者: 朱红宝
  • 作者简介:朱红宝(通讯作者),男,1975年生,硕士/讲师.研究方向:微分方程的渐近理论.E-mail: zhuhb@ahut.edu.cn
  • 基金资助:
    安徽省高校自然科学研究重点项目(KJ2019A0062)资助.

The shock solution to a class of nonlinear singularly perturbed boundary value problems with time delay

ZHU Hongbao, CHEN Songlin, DU Yajie   

  1. School of Mathematics and Physics, Anhui University of Technology, Maanshan 243002,China
  • Received:2019-06-18 Revised:2019-07-24 Accepted:2019-07-24 Online:2020-02-28 Published:2019-07-24

摘要: 讨论了一类非线性奇异摄动时滞问题的激波解,利用匹配渐近展开法得出了问题解的展开式,并利用微分不等式理论证明了解的一致有效性,最后通过实例验证了所提问题激波解的存在性.

关键词: 非线性, 奇摄动, 时滞, 激波解

Abstract: The shock solution for a class of singularly perturbed time delay nonlinear problem were studied .The solution was obtained by using the matching asymptotic expansion,and the uniform validity of the shock solution of the problem was proved by the theory of differential inequalities .Finally, an example was given to verify the existence of the shock solution.

Key words: nonlinear, singularly perturbed, time delay, shock solution

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