棱柱体中调和方程对基底扰动的连续依赖性

数学物理学报 ›› 2025, Vol. 45 ›› Issue (1): 101-109.

棱柱体中调和方程对基底扰动的连续依赖性

陈雪姣^*, 李丹丹, 石金诚, 曾鹏

广州华商学院应用数学系广州 511300

收稿日期:2023-10-08 修回日期:2024-04-08 出版日期:2025-02-26 发布日期:2025-01-08
通讯作者: *陈雪姣, E-mail:A10314063@163.com
作者简介:李丹丹, E-mail:li20201101@126.com; 石金诚, E-mail:hning0818@163.com; 曾鹏, E-mail:m18819484746@163.com
基金资助:
国家自然科学基金 (11371175) 和广州华商学院导师制项目 (2023HSDS29)

Continuous Dependence of Harmonic Equations on Base Perturbation in Prismatic Cylinder

Chen Xuejiao, Li Dandan, Shi Jincheng, Zeng Peng

Department of Apllied Mathematics, Guangzhou Huashang College, Guangzhou 511300

Received:2023-10-08 Revised:2024-04-08 Online:2025-02-26 Published:2025-01-08
Supported by:
NSFC (11371175) and the Tutorial Program of Guangzhou Huashang College (2023HSDS29)

摘要/Abstract

摘要： 该文研究定义在基底受到扰动的半无限圆柱体内的调和方程对基本几何结构和衰减行为的连续依赖关系. 假设在柱体的侧面上调和方程满足齐次边界条件,利用微分不等式技术, 推导出了一个关于几何基底的扰动和解的差异的微分不等式. 该微分不等式可以直接推导出解对扰动参数和基底上已知数据的连续依赖性.

关键词: 调和方程, 扰动, 连续依赖性, 微分方程

Abstract: This article establishes the continuous dependence of the harmonic equation on its basic geometry and load of the decay behaviour in a prismatic semi-infinite cylinder. Assuming that the harmonic equation on the side of the cylinder satisfies homogeneous boundary conditions, a differential inequality technique is used to derive a differential inequality for perturbation of geometric bases and differences in solutions. This differential inequality can directly derive the continuous dependence of the solution on perturbation parameters and known data on the base.

Key words: harmonic equation, perturbation, continuous dependence, differential equation

中图分类号:

O175.29

陈雪姣, 李丹丹, 石金诚, 曾鹏. 棱柱体中调和方程对基底扰动的连续依赖性[J]. 数学物理学报, 2025, 45(1): 101-109.

Chen Xuejiao, Li Dandan, Shi Jincheng, Zeng Peng. Continuous Dependence of Harmonic Equations on Base Perturbation in Prismatic Cylinder[J]. Acta mathematica scientia,Series A, 2025, 45(1): 101-109.

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