具有延迟边界反馈的退化/奇异双曲型方程的指数稳定性

IF 1 4区数学 Q2 MATHEMATICS, APPLIED

Acta Applicandae Mathematicae Pub Date : 2025-06-19 DOI:10.1007/s10440-025-00737-7

Jawad Salhi

{"title":"具有延迟边界反馈的退化/奇异双曲型方程的指数稳定性","authors":"Jawad Salhi","doi":"10.1007/s10440-025-00737-7","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we consider a degenerate/singular wave equation that is fixed at the point where the degeneracy occurs and stabilized with a time-delayed boundary feedback at the other endpoint. First, we study the well-posedness of the system under consideration in appropriate weighted spaces by using semigroup theory. Then, we prove its exponential stability under a suitable condition on both coefficients of the delayed damping term and the not delayed one. Furthermore, an explicit expression of the exponential decay in terms of the system parameters is provided, leveraging both the multiplier method and the Lyapunov functional approach.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"198 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Exponential Stability for Degenerate/Singular Hyperbolic Equations with Delayed Boundary Feedback\",\"authors\":\"Jawad Salhi\",\"doi\":\"10.1007/s10440-025-00737-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we consider a degenerate/singular wave equation that is fixed at the point where the degeneracy occurs and stabilized with a time-delayed boundary feedback at the other endpoint. First, we study the well-posedness of the system under consideration in appropriate weighted spaces by using semigroup theory. Then, we prove its exponential stability under a suitable condition on both coefficients of the delayed damping term and the not delayed one. Furthermore, an explicit expression of the exponential decay in terms of the system parameters is provided, leveraging both the multiplier method and the Lyapunov functional approach.</p></div>\",\"PeriodicalId\":53132,\"journal\":{\"name\":\"Acta Applicandae Mathematicae\",\"volume\":\"198 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2025-06-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Applicandae Mathematicae\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10440-025-00737-7\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Applicandae Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10440-025-00737-7","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

在本文中，我们考虑一个简并/奇异波动方程，它在简并发生的点是固定的，在另一个点有一个时滞边界反馈稳定。首先，利用半群理论研究了给定系统在适当加权空间中的适定性。然后，在适当的条件下，证明了时滞阻尼项系数和非时滞阻尼项系数的指数稳定性。此外，利用乘数法和李雅普诺夫泛函方法，给出了系统参数的指数衰减的显式表达式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Exponential Stability for Degenerate/Singular Hyperbolic Equations with Delayed Boundary Feedback

In this paper, we consider a degenerate/singular wave equation that is fixed at the point where the degeneracy occurs and stabilized with a time-delayed boundary feedback at the other endpoint. First, we study the well-posedness of the system under consideration in appropriate weighted spaces by using semigroup theory. Then, we prove its exponential stability under a suitable condition on both coefficients of the delayed damping term and the not delayed one. Furthermore, an explicit expression of the exponential decay in terms of the system parameters is provided, leveraging both the multiplier method and the Lyapunov functional approach.

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

Acta Applicandae Mathematicae 数学-应用数学

CiteScore

2.80

自引率

6.20%

发文量

审稿时长

16.2 months

期刊介绍： Acta Applicandae Mathematicae is devoted to the art and techniques of applying mathematics and the development of new, applicable mathematical methods. Covering a large spectrum from modeling to qualitative analysis and computational methods, Acta Applicandae Mathematicae contains papers on different aspects of the relationship between theory and applications, ranging from descriptive papers on actual applications meeting contemporary mathematical standards to proofs of new and deep theorems in applied mathematics.