华东师范大学学报（自然科学版） >

2020 , Vol. 2020 >Issue 2: 23 - 34

DOI: https://doi.org/10.3969/j.issn.1000-5641.201911043

数学

具有罗宾边值条件的一类奇摄动微分方程的内部层

  • 德米 ,
  • 倪明康
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  • 华东师范大学 数学科学学院, 上海　200241
德米,男,博士研究生,研究方向为应用数学.E-mail:mitichya@yandex.ru

收稿日期: 2019-10-17

  网络出版日期: 2020-03-16

基金资助

国家自然科学基金（11871217）

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Internal layers for a singularly perturbed differential equation with Robin boundary value condition

  • CHAIKOVSKII Dmitrii ,
  • Mingkang NI
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  • School of Mathematical Sciences, East China Normal University, Shanghai　200241, China

Received date: 2019-10-17

  Online published: 2020-03-16

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摘要

本文研究了一类具有罗宾边值条件的二阶奇摄动右端不连续微分方程, 用边界层函数法构造了该类方程解的渐近表达式, 最后用缝接法证明了该问题解的存在性, 并给出了渐近解的余项估计.

关键词： 奇摄动; 渐近表达式; 罗宾边值条件; 内部层

本文引用格式

德米 , 倪明康 . 具有罗宾边值条件的一类奇摄动微分方程的内部层[J]. 华东师范大学学报（自然科学版）, 2020 , 2020(2) : 23 -34 . DOI: 10.3969/j.issn.1000-5641.201911043

Abstract

In this paper, we consider a second order singularly perturbed equation with a discontinuous right-hand function and Robin boundary value condition. Applying the boundary layer function method, we can construct an asymptotical approximation of the solution. We also prove the existence of the solution and obtain an estimation of the remainder based on the matching method.

Key words： singular perturbation; asymptotic approximation; Robin boundary value condition; internal layer

参考文献

[1] NEFEDOV N N, NI M K. The inner layers in the one-dimensional reaction-diffusion equation with a discontinuous reactive term[J]. Journal of Computational Mathematics and Mathematical Physics, 2015, 55(12):2042-2048.
[2] LEVASHOV N T, NEFEDOV N N, ORLOV A O. Stationary reaction-diffusion equation with a discontinuous reactive term[J]. Journal of Computational Mathematics and Mathematical Physics, 2017, 57(5):854-866. DOI:10.1134/S0965542517050062.
[3] VASILYEVA A B, BUTUZOV V F, NEFEDOV N N. Singularly perturbed problems with boundary inner layers[J]. Proceedings of the Steklov Mathematical Institute, Russian Academy of Sciences, 2010, 268:268-283.
[4] VOLKOV V, NEFEDOV N N. Asymptotic-numerical investigation of generation and motion of fronts in phase transition models[M]//. Numerical Analysis and Its Applications. Berlin:Springer-Verlag, 2012:524-531.
[5] VASILYEVA A B, BUTUZOV V F. Asymptotic Methods in the Theory of Singular Perturbations[M]. Moscow:Higher School, 1990:208.
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