奇异摄动积分边值问题中的空间对照结构

数学物理学报 ›› 2025, Vol. 45 ›› Issue (5): 1565-1576.

奇异摄动积分边值问题中的空间对照结构

武利猛^1,²(),李素红¹(),倪明康^3,^*(),陆海波⁴()

¹河北科技师范学院数学与信息科技学院河北秦皇岛 066004
²河北省海洋动力过程与资源环境重点实验室河北秦皇岛 066004
³华东师范大学数学科学学院上海 200241
⁴上海应用技术大学经管学院上海 201418

收稿日期:2022-08-25 修回日期:2024-01-10 出版日期:2025-10-26 发布日期:2025-10-14
通讯作者: * 倪明康,E-mail:xiaovikdo@163.com
作者简介:武利猛,E-mail:neamou123@163.com|李素红,E-mail:lisuhong103@126.com|陆海波, E-mail:hblu1985@163.com
基金资助:
国家自然科学基金(11871217);国家自然科学基金(11901152);国家自然科学基金(72371097)

Contrast Structure of Singularly Perturbed Integral Boundary Value Problem

Limeng Wu^1,²(),Suhong Li¹(),Mingkang Ni^3,^*(),Haibo Lu⁴()

¹School of Mathematics and Information Technology, Hebei Normal University of Science and Technology, Hebei Qinhuangdao 066004
²Hebei Key Laboratory of Ocean Dynamics, Resources and Environments, Hebei Qinhuangdao 066004
³School of Mathematical Sciences, East China Normal University, Shanghai 200241
⁴School of Economics and Management, Shanghai Institute of Technology, Shanghai 201418

Received:2022-08-25 Revised:2024-01-10 Online:2025-10-26 Published:2025-10-14
Supported by:
NSFC(11871217);NSFC(11901152);NSFC(72371097)

摘要/Abstract

摘要：

该文研究了一类带有积分边界条件的奇异摄动边值问题的空间对照结构, 利用奇异摄动几何理论和微积分技巧, 证明了等价边值问题阶梯状空间对照结构解的存在性. 基于解的结构, 利用边界层函数法构造了一致有效的形式渐近解. 通过一个例子, 验证了主要结果.

关键词: 奇异摄动, 渐近解, 空间对照结构

Abstract:

In this paper, we consider the contrast structure solution for singularly perturbed boundary value problem with integral boundary condition. By using geometric singular perturbation theory, as well as analysis technique, we first establish the existence result of step-like contrast structure solution for the corresponding equivalent boundary value problem. Furthermore, by virtue of the structure of the solution, we construct the uniformly valid formal asymptotic solution by the boundary function method. Finally, an example is given to show the main result.

Key words: singular perturbation, asymptotic solution, contrast structure

中图分类号:

O175.14

武利猛, 李素红, 倪明康, 陆海波. 奇异摄动积分边值问题中的空间对照结构[J]. 数学物理学报, 2025, 45(5): 1565-1576.

Limeng Wu, Suhong Li, Mingkang Ni, Haibo Lu. Contrast Structure of Singularly Perturbed Integral Boundary Value Problem[J]. Acta mathematica scientia,Series A, 2025, 45(5): 1565-1576.

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