一类右端不连续奇异摄动高阶方程组的内部层

数学物理学报 ›› 2024, Vol. 44 ›› Issue (5): 1153-1166.

一类右端不连续奇异摄动高阶方程组的内部层

傅越宸(),倪明康^*()

华东师范大学数学科学学院上海 200241

收稿日期:2023-11-01 修回日期:2024-04-01 出版日期:2024-10-26 发布日期:2024-10-16
通讯作者: *倪明康, E-mail: xiaovikdo@163.com
作者简介:傅越宸, E-mail: fuyuechenwflms@163.com
基金资助:
国家自然科学基金(12371168);上海市科学技术委员会基金(18dz2271000)

The Inner Layer of a Class of Singularly Perturbed High-Order Equations with Discontinuous Right-Hand Side

Fu Yuechen(),Ni Mingkang^*()

School of Mathematical Sciences, East China Normal University, Shanghai 200241

Received:2023-11-01 Revised:2024-04-01 Online:2024-10-26 Published:2024-10-16
Supported by:
NSFC(12371168);Science and Technology Commission of Shanghai Municipality(18dz2271000)

摘要/Abstract

摘要：

该文介绍了关于右端不连续奇摄动问题的一些工作, 主要讨论了一类具有 Dirichlet 边值条件的右端不连续四阶奇摄动方程, 引入复方程形式后, 运用边界层函数法构造了具有内部转移层的形式渐近解, 并给出了光滑解的存在性与余项估计. 最后给出一个例子来验证算法的正确性.

关键词: 奇异摄动系统, 右端不连续, 空间对照结构, 边界层函数法, 光滑缝接

Abstract:

This paper introduces some work on singular perturbation problems with discontinuous right-hand side, mainly discusses a class of fourth-order Dirichlet boundary value singular perturbation equations with discontinuous right-hand sides. After introducing complex equation form, we construct a formal asymptotic solution with an internal transfer layer by using the boundary layer function method, and give the existence and residual estimation of smooth solutions. Finally, an example is given to verify the correctness of the algorithm.

Key words: Singularly perturbed system, Discontinuous right-hand side, Spatial contrast structure, Boundary layer function method, Smooth joint

中图分类号:

O175.14

傅越宸, 倪明康. 一类右端不连续奇异摄动高阶方程组的内部层[J]. 数学物理学报, 2024, 44(5): 1153-1166.

Fu Yuechen, Ni Mingkang. The Inner Layer of a Class of Singularly Perturbed High-Order Equations with Discontinuous Right-Hand Side[J]. Acta mathematica scientia,Series A, 2024, 44(5): 1153-1166.

图/表 4

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