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);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);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.

参考文献

[1]	Smale S, Hirsch M W. Differential Equations Dynamical Systems, and Linear Algebra. New York: Academic Press, 1974
[2]	Knops R J, Payne L E. The effect of a variation in the elastic moduli on Saint-Venant's principle for a half-cylinder. J Elasticity, 1996, 44(2): 161-182
[3]	Li Y F, Lin C H. Continuous dependence for the nonhomogeneous Brinkman-Forchheimer equations in a semi-infinite pipe. Applied Mathematics and Computation, 2014, 244: 201-208
[4]	李远飞, 肖胜中, 曾鹏. 饱和蒸汽大气原始方程组的连续依赖性. 华东师范大学学报 (自然科学版), 2021, 2021(3): 34-46
[4]	Li Y F, Xiao S Z, Zeng P. Continuous dependence of primitive equations of the atmosphere with vapor saturation. Journal of East China Normal University (Natural Science), 2021, 2021(3): 34-46
[5]	Franchi F, Nibbi R, Straughan B. Continuous dependence on modelling for temperature-dependent bidispersive flow. Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences, 2017, 473(2208): 20170485
[6]	Ciarletta M, Straughan B, Tibullo V. Structural stability for a thermal convection model with temperature-dependent solubility. Nonlinear Analysis: Real World Applications, 2015, 22: 34-43
[7]	Li Y F, Chen X J. Structural stability for temperature-dependent bidispersive flow in a semi-infinite pipe. Lithuanian Mathematical Journal, 2023, 63(3): 337-366
[8]	李远飞. Keller-Segel 趋化模型解的全局存在性和爆破时间的下界估计. 应用数学和力学, 2022, 43(7): 816-824
[8]	Li Y F. Global existence of solutions and lower bound estimate of blow-up time for the Keller-Segel chemotaxis model. Applied Mathematics and Mechanics, 2022, 43(7): 816-824
[9]	Payne L E, Song J C. Spatial decay estimates for the Brinkman and Darcy flows in a semi-infinite cylinder. Contin Mech Thermodyn, 1997, 9(3): 175-190
[10]	Hardy G H, Littlewood J E, Pólya G. Inequalities. Cambridge: Cambridge University Press, 1952
[11]	Horgan C O, Payne L E. Phragmén-Lindel?f type results for harmonic functions with nonlinear boundary conditions. Arch Rational Mech Anal, 1993, 122(2): 123-144

[1]	曾夏萍, 卢文雯, 庞国萍, 梁志清. 具有季节性切换反应及脉冲扰动的鱼类单种群动力学模型[J]. 数学物理学报, 2025, 45(4): 1206-1216.
[2]	张胜良, 钱艳艳. 随机扰动下三阶MQ拟插值在导数逼近中的应用研究[J]. 数学物理学报, 2025, 45(1): 180-188.
[3]	韦华全, 吴辉, 刘晓冀, 靳宏伟. $\mathfrak{m}$-WG 逆的性质和计算[J]. 数学物理学报, 2024, 44(3): 547-562.
[4]	廖远康. 粘性依赖于密度的一维等熵可压缩 Navier-Stokes 方程组粘性激波的非线性稳定性[J]. 数学物理学报, 2023, 43(4): 1149-1169.
[5]	建芒芒, 郑素佩, 封建湖, 翟梦情. 浅水波方程熵稳定格式的保平衡性[J]. 数学物理学报, 2023, 43(2): 491-504.
[6]	白晓瑾,朱剑峰. 一族非齐次双调和方程解的边界Schwarz引理[J]. 数学物理学报, 2022, 42(6): 1633-1639.
[7]	聂嘉乐,余旌胡. 一类受随机扰动的动态优化问题的环境检测与响应[J]. 数学物理学报, 2022, 42(5): 1560-1574.
[8]	范楠,王才士,姬红. Bernoulli泛函上典则酉对合的扰动[J]. 数学物理学报, 2022, 42(4): 969-977.
[9]	李远飞,石金诚,朱慧珊,黄诗淇. 热弹性方程的快速增长或衰减估计[J]. 数学物理学报, 2021, 41(4): 1042-1052.
[10]	张仲华,张倩. 转换机制下具有非线性扰动的随机SIVS传染病模型的定性分析[J]. 数学物理学报, 2021, 41(4): 1218-1234.
[11]	佟玉霞,王薪茹,谷建涛. Orlicz空间中A-调和方程很弱解得L^ϕ估计[J]. 数学物理学报, 2020, 40(6): 1461-1480.
[12]	李海侠. 一类具有毒素的非均匀chemostat模型正解的存在性和唯一性[J]. 数学物理学报, 2020, 40(5): 1175-1185.
[13]	包贵,孙倩. 一类次线性双调和方程变号解的存在性与多重性[J]. 数学物理学报, 2020, 40(5): 1186-1191.
[14]	梁文翠,张正杰. Kirchhoff型方程有关的非线性方程多解的存在性[J]. 数学物理学报, 2020, 40(4): 842-849.
[15]	杜志华,李玉妹. 二维Lipschitz区域上一类带L^p[J]. 数学物理学报, 2020, 40(2): 271-287.