具有高阶转动惯量和非局部阻尼的高阶((m_{1},m_{2})耦合基尔霍夫模型解的长期动力学特性

IF 1.7 4区 数学 Q1 Mathematics
Penghui Lv, Yuan Yuan, Guoguang Lin
{"title":"具有高阶转动惯量和非局部阻尼的高阶((m_{1},m_{2})耦合基尔霍夫模型解的长期动力学特性","authors":"Penghui Lv, Yuan Yuan, Guoguang Lin","doi":"10.1186/s13661-024-01857-z","DOIUrl":null,"url":null,"abstract":"The Kirchhoff model is derived from the vibration problem of stretchable strings. This paper focuses on the longtime dynamics of a higher-order $(m_{1},m_{2})$ -coupled Kirchhoff system with higher-order rotational inertia and nonlocal damping. We first obtain the state of the model’s solutions in different spaces through prior estimation. After that, we immediately prove the existence and uniqueness of their solutions in different spaces through the Faedo-Galerkin method. Subsequently, we prove their family of global attractors using the compactness theorem. Finally, we reflect on the subsequent research of the model and point out relevant directions for further research on the model. In this way, we systematically study the longtime dynamics of the higher-order $(m_{1},m_{2})$ -coupled Kirchhoff model with higher-order rotational inertia, thus enriching the relevant findings of higher-order coupled Kirchhoff models and laying a theoretical foundation for future practical applications.","PeriodicalId":49228,"journal":{"name":"Boundary Value Problems","volume":"166 1","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Longtime dynamics of solutions for higher-order \\\\((m_{1},m_{2})\\\\)-coupled Kirchhoff models with higher-order rotational inertia and nonlocal damping\",\"authors\":\"Penghui Lv, Yuan Yuan, Guoguang Lin\",\"doi\":\"10.1186/s13661-024-01857-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Kirchhoff model is derived from the vibration problem of stretchable strings. This paper focuses on the longtime dynamics of a higher-order $(m_{1},m_{2})$ -coupled Kirchhoff system with higher-order rotational inertia and nonlocal damping. We first obtain the state of the model’s solutions in different spaces through prior estimation. After that, we immediately prove the existence and uniqueness of their solutions in different spaces through the Faedo-Galerkin method. Subsequently, we prove their family of global attractors using the compactness theorem. Finally, we reflect on the subsequent research of the model and point out relevant directions for further research on the model. In this way, we systematically study the longtime dynamics of the higher-order $(m_{1},m_{2})$ -coupled Kirchhoff model with higher-order rotational inertia, thus enriching the relevant findings of higher-order coupled Kirchhoff models and laying a theoretical foundation for future practical applications.\",\"PeriodicalId\":49228,\"journal\":{\"name\":\"Boundary Value Problems\",\"volume\":\"166 1\",\"pages\":\"\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-04-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Boundary Value Problems\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1186/s13661-024-01857-z\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Boundary Value Problems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1186/s13661-024-01857-z","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0

摘要

基尔霍夫模型源于可拉伸弦的振动问题。本文主要研究具有高阶转动惯量和非局部阻尼的高阶$(m_{1},m_{2})$耦合基尔霍夫系统的长期动力学。我们首先通过先验估计获得模型解在不同空间的状态。之后,我们立即通过 Faedo-Galerkin 方法证明其在不同空间的解的存在性和唯一性。随后,我们利用紧凑性定理证明了它们的全局吸引子族。最后,我们对该模型的后续研究进行了反思,并指出了进一步研究该模型的相关方向。这样,我们系统地研究了具有高阶转动惯量的高阶$(m_{1},m_{2})$耦合基尔霍夫模型的长期动力学,从而丰富了高阶耦合基尔霍夫模型的相关研究成果,为今后的实际应用奠定了理论基础。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Longtime dynamics of solutions for higher-order \((m_{1},m_{2})\)-coupled Kirchhoff models with higher-order rotational inertia and nonlocal damping
The Kirchhoff model is derived from the vibration problem of stretchable strings. This paper focuses on the longtime dynamics of a higher-order $(m_{1},m_{2})$ -coupled Kirchhoff system with higher-order rotational inertia and nonlocal damping. We first obtain the state of the model’s solutions in different spaces through prior estimation. After that, we immediately prove the existence and uniqueness of their solutions in different spaces through the Faedo-Galerkin method. Subsequently, we prove their family of global attractors using the compactness theorem. Finally, we reflect on the subsequent research of the model and point out relevant directions for further research on the model. In this way, we systematically study the longtime dynamics of the higher-order $(m_{1},m_{2})$ -coupled Kirchhoff model with higher-order rotational inertia, thus enriching the relevant findings of higher-order coupled Kirchhoff models and laying a theoretical foundation for future practical applications.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Boundary Value Problems
Boundary Value Problems MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
3.00
自引率
5.90%
发文量
83
审稿时长
4 months
期刊介绍: The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信