具有 Balakrishnan-Taylor、强和局部非线性阻尼的可扩展梁方程的指数稳定性

IF 0.7 3区 数学 Q2 MATHEMATICS
Zayd Hajjej
{"title":"具有 Balakrishnan-Taylor、强和局部非线性阻尼的可扩展梁方程的指数稳定性","authors":"Zayd Hajjej","doi":"10.1007/s00233-024-10419-9","DOIUrl":null,"url":null,"abstract":"<p>We study a nonlinear Cauchy problem modeling the motion of an extensible beam </p><span>$$\\begin{aligned} \\vert y_t\\vert ^{r}y_{tt}{} &amp; {} +\\gamma \\Delta ^2 y_{tt}+\\Delta ^2y-\\left( a+b\\vert \\vert \\nabla y\\vert \\vert ^2+c (\\nabla y, \\nabla y_t)\\right) \\Delta y\\\\{} &amp; {} \\quad +\\Delta ^2 y_t+ d(x)h(y_t)+f(y)=0, \\end{aligned}$$</span><p>in a bounded domain of <span>\\(\\mathbb {R}^N\\)</span>, with clamped boundary conditions in either cases: when <span>\\(r=\\gamma =0\\)</span> or else when <i>r</i> and <span>\\(\\gamma \\)</span> are positive. We prove, in both cases, the existence of solutions and the exponential decay of energy.</p>","PeriodicalId":49549,"journal":{"name":"Semigroup Forum","volume":"12 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Exponential stability of extensible beams equation with Balakrishnan–Taylor, strong and localized nonlinear damping\",\"authors\":\"Zayd Hajjej\",\"doi\":\"10.1007/s00233-024-10419-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We study a nonlinear Cauchy problem modeling the motion of an extensible beam </p><span>$$\\\\begin{aligned} \\\\vert y_t\\\\vert ^{r}y_{tt}{} &amp; {} +\\\\gamma \\\\Delta ^2 y_{tt}+\\\\Delta ^2y-\\\\left( a+b\\\\vert \\\\vert \\\\nabla y\\\\vert \\\\vert ^2+c (\\\\nabla y, \\\\nabla y_t)\\\\right) \\\\Delta y\\\\\\\\{} &amp; {} \\\\quad +\\\\Delta ^2 y_t+ d(x)h(y_t)+f(y)=0, \\\\end{aligned}$$</span><p>in a bounded domain of <span>\\\\(\\\\mathbb {R}^N\\\\)</span>, with clamped boundary conditions in either cases: when <span>\\\\(r=\\\\gamma =0\\\\)</span> or else when <i>r</i> and <span>\\\\(\\\\gamma \\\\)</span> are positive. We prove, in both cases, the existence of solutions and the exponential decay of energy.</p>\",\"PeriodicalId\":49549,\"journal\":{\"name\":\"Semigroup Forum\",\"volume\":\"12 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-03-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Semigroup Forum\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00233-024-10419-9\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Semigroup Forum","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00233-024-10419-9","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

摘要

我们研究了一个模拟可伸展梁运动的非线性考奇问题 $$\begin{aligned}\vert y_t\vert ^{r}y_{tt}{} & {}+\gamma \Delta ^2 y_{tt}+\Delta ^2y-\left( a+b\vert \vert \vert \vert ^2+c (\nabla y, \nabla y_t)\right) \Delta y\{} & {}\quad +\Delta ^2 y_t+ d(x)h(y_t)+f(y)=0, \end{aligned}$$ in a bounded domain of \(\mathbb {R}^N\), with clamped boundary conditions in either cases: when \(r=\gamma =0\) or else when r and\(\gamma \) are positive.在这两种情况下,我们都证明了解的存在和能量的指数衰减。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Exponential stability of extensible beams equation with Balakrishnan–Taylor, strong and localized nonlinear damping

We study a nonlinear Cauchy problem modeling the motion of an extensible beam

$$\begin{aligned} \vert y_t\vert ^{r}y_{tt}{} & {} +\gamma \Delta ^2 y_{tt}+\Delta ^2y-\left( a+b\vert \vert \nabla y\vert \vert ^2+c (\nabla y, \nabla y_t)\right) \Delta y\\{} & {} \quad +\Delta ^2 y_t+ d(x)h(y_t)+f(y)=0, \end{aligned}$$

in a bounded domain of \(\mathbb {R}^N\), with clamped boundary conditions in either cases: when \(r=\gamma =0\) or else when r and \(\gamma \) are positive. We prove, in both cases, the existence of solutions and the exponential decay of energy.

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
Semigroup Forum
Semigroup Forum 数学-数学
CiteScore
1.50
自引率
14.30%
发文量
79
审稿时长
12 months
期刊介绍: Semigroup Forum is a platform for speedy and efficient transmission of information on current research in semigroup theory. Scope: Algebraic semigroups, topological semigroups, partially ordered semigroups, semigroups of measures and harmonic analysis on semigroups, numerical semigroups, transformation semigroups, semigroups of operators, and applications of semigroup theory to other disciplines such as ring theory, category theory, automata, logic, etc. Languages: English (preferred), French, German, Russian. Survey Articles: Expository, such as a symposium lecture. Of any length. May include original work, but should present the nonspecialist with a reasonably elementary and self-contained account of the fundamental parts of the subject. Research Articles: Will be subject to the usual refereeing procedure. Research Announcements: Description, limited to eight pages, of new results, mostly without proofs, of full length papers appearing elsewhere. The announcement must be accompanied by a copy of the unabridged version. Short Notes: (Maximum 4 pages) Worthy of the readers'' attention, such as new proofs, significant generalizations of known facts, comments on unsolved problems, historical remarks, etc. Research Problems: Unsolved research problems. Announcements: Of conferences, seminars, and symposia on Semigroup Theory. Abstracts and Bibliographical Items: Abstracts in English, limited to one page, of completed work are solicited. Listings of books, papers, and lecture notes previously published elsewhere and, above all, of new papers for which preprints are available are solicited from all authors. Abstracts for Reviewing Journals: Authors are invited to provide with their manuscript informally a one-page abstract of their contribution with key words and phrases and with subject matter classification. This material will be forwarded to Zentralblatt für Mathematik.
×
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