一类动态Melan方程的解的存在唯一性

唐梦影; 张健; 王永达

doi:10.3969/j.issn.1000-1565.2022.05.001

河北大学学报(自然科学版) >

2022 , Vol. 42 >Issue 5: 449 - 453

DOI: https://doi.org/10.3969/j.issn.1000-1565.2022.05.001

一类动态Melan方程的解的存在唯一性

唐梦影 ,
张健 ,
王永达

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唐梦影(1996—),女,河北沧州人,河北大学在读硕士研究生,主要从事偏微分方程研究.
E-mail: 1546309993@qq.com

收稿日期: 2022-03-01

网络出版日期: 2022-10-19

基金资助

河北省自然科学基金资助项目(A2019201106);河北大学高层次人才引进项目(521000981097)

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Existence and uniqueness of solutions for a class of dynamic Melan equations

TANG Mengying ,
ZHANG Jian ,
WANG Yongda

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Hebei Key Laboratory of Machine Learning and Computational Intelligence, College of Mathematics and Information Science, Hebei University, Baoding 071002, China

Received date: 2022-03-01

Online published: 2022-10-19

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摘要

为解决悬索桥的动态横梁模型——动态Melan方程的问题,采用Galerkin方法和压缩映射原理,对这类非线性非局部Melan方程进行了研究,得出了该方程的解的存在唯一性.

关键词： Melan方程; Galerkin方法; 悬索桥

本文引用格式

唐梦影 , 张健 , 王永达 . 一类动态Melan方程的解的存在唯一性[J]. 河北大学学报(自然科学版), 2022 , 42(5) : 449 -453 . DOI: 10.3969/j.issn.1000-1565.2022.05.001

Abstract

To solve a dynamic Melan equation, which is viewed as a beam model for dynamic suspension bridges, Galerkin’s method and the contraction mapping principle are applied to the nonlinear non-local Melan equation. The existence and uniqueness results are obtained.

Key words： Melan equation; Galerkin’s method; suspension bridge

参考文献

[1] GAZZOLA F, WANG Y D, PAVANI R. Variational formulation of the Melan equation[J]. Math Meth Appl Sci, 2018, 41(3): 943-951. DOI:10.1002/mma.3962.
[2] MELAN J. Theory of arches and suspension bridge[M]. London:Myron Clark Pul,1913.
[3] GAZZOLA F, JLELI M, SAMET B. On the Melan equation for suspension bridges[J]. J Fixed Point Theory Appl, 2014, 16(1/2): 159-188. DOI:10.1007/s11784-014-0200-5.
[4] GAZZOLA F, SPERONE G. Thresholds for hanger slackening and cable shortening in the Melan equation for suspension bridges[J]. Nonlinear Anal Real World Appl, 2018, 39: 520-536. DOI:10.1016/j.nonrwa.2017.08.001.
[5] FALOCCHI A. Torsional instability and sensitivity analysis in a suspension bridge model related to the Melan equation[J]. Commun Nonlinear Sci Numer Simul, 2019, 67: 60-75. DOI:10.1016/j.cnsns.2018.07.005.
[6] ARIOLI G, GAZZOLA F. On a nonlinear nonlocal hyperbolic system modeling suspension bridges[J]. Milan J Math, 2015, 83(2): 211-236. DOI:10.1007/s00032-015-0239-9.
[7] 王高雄, 周之铭, 朱思铭. 常微分方程[M]. 3版. 北京: 高等教育出版社, 2006. (

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