一类弱非线性临界奇摄动积分边界问题

数学物理学报 ›› 2022, Vol. 42 ›› Issue (4): 1060-1073.

一类弱非线性临界奇摄动积分边界问题

张浩(),汪娜*()

上海应用技术大学理学院上海 201418

收稿日期:2021-08-17 出版日期:2022-08-26 发布日期:2022-08-08
通讯作者: 汪娜 E-mail:1173934437@qq.com;wangna1621@126.com
作者简介:张浩, E-mail: 1173934437@qq.com
基金资助:
上海应用技术大学自然科学项目(1021GK210006141)

A Class of Weakly Nonlinear Critical Singularly Perturbed Integral Boundary Problems

Hao Zhang(),Na Wang*()

College of Sciences, Shanghai Institute of Technology, Shanghai 201418

Received:2021-08-17 Online:2022-08-26 Published:2022-08-08
Contact: Na Wang E-mail:1173934437@qq.com;wangna1621@126.com
Supported by:
the Nature Science Fund of Shanghai Institute of Technology(1021GK210006141)

摘要/Abstract

摘要：

基于边界层函数法, 研究了一类弱非线性临界情况下的带有积分边界条件的奇异摄动问题. 在该文的框架下, 作者不仅构造了原方程解的渐近展开式, 还给出了一致有效渐近展开式的证明. 同时, 该文给出了一个例子来说明文中的结果, 并且画出了近似解与精确解在不同小参数下比较的图像.

关键词: 临界情况, 奇异摄动, 边界层函数法, 近似解

Abstract:

Based on the boundary layer function method, a class of singularly perturbed problems with integral boundary conditions in weakly nonlinear critical cases are studied. In the framework of this paper, we not only construct the asymptotic expansion of the solution of the original equation, but also prove the uniformly effective asymptotic expansion. At the same time, we give an example to illustrate our results, The comparison images of approximate solution and exact solution under different small parameters are drawn.

Key words: Critical situation, Singular perturbation, Boundary layer function method, Approximate solution

中图分类号:

O175.14

张浩,汪娜. 一类弱非线性临界奇摄动积分边界问题[J]. 数学物理学报, 2022, 42(4): 1060-1073.

Hao Zhang,Na Wang. A Class of Weakly Nonlinear Critical Singularly Perturbed Integral Boundary Problems[J]. Acta mathematica scientia,Series A, 2022, 42(4): 1060-1073.

图/表 2

参考文献 12

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