一类二阶双参数非线性时滞问题的奇摄动

朱红宝; 陈松林

doi:10.21656/1000-0887.410082

一类二阶双参数非线性时滞问题的奇摄动

doi: 10.21656/1000-0887.410082

安徽工业大学数理科学与工程学院, 安徽马鞍山 243002

基金项目: 安徽省高校自然科学研究重点项目(KJ2019A0062)

详细信息

作者简介:
朱红宝(1975—),男,讲师,硕士(通讯作者. E-mail: zhuhb@ahut.edu.cn).

中图分类号: O175.14
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- 被引次数: 0
出版历程
- 收稿日期: 2020-03-17
- 修回日期: 2020-04-17
- 刊出日期: 2020-11-01

A Class of 2nd-Order Singularly Perturbed Time Delay Nonlinear Problems With 2 Parameters

School of Mathematics & Physics, Anhui University of Technology, Maanshan, Anhui 243002, P.R.China

摘要

摘要: 该文讨论了一类含有两个参数的非线性时滞问题，利用奇异摄动方法，研究了当两个参数满足一定关系时，所提问题的渐近解的性态.首先利用奇异摄动方法求出了问题的外部解;再利用伸展变量法构造了问题在边界附近的边界层校正项，得出了所提问题的形式渐近解;最后，在合适的假设条件下，利用微分不等式理论证明了解的一致有效性.
- 非线性 /
- 奇摄动 /
- 双参数 /
- 时滞
Abstract: A class of 2nd-order singularly perturbed time delay nonlinear problems were considered. The asymptotic solution to the problem was obtained with the singular perturbation method. Firstly, The outer solution was constructed by means of the singular perturbation method. Then, a stretched variable was introduced, the boundary layer correction of the solution was obtained, and the asymptotic analytic expansion solution to the problem was also given. Finally, under suitable conditions, the theory of differential inequalities was applied to prove the uniformly valid asymptotic expansion of the solution to the original problem.
- nonlinear /
- singularly perturbed /
- 2 parameters /
- time delay

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参考文献(12)

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