Bresse系统的点态稳定

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED

Zeitschrift fur Angewandte Mathematik und Physik Pub Date : 2023-10-13 DOI:10.1007/s00033-023-02108-4

Jaime E. Muñoz Rivera, Maria Grazia Naso

{"title":"Bresse系统的点态稳定","authors":"Jaime E. Muñoz Rivera, Maria Grazia Naso","doi":"10.1007/s00033-023-02108-4","DOIUrl":null,"url":null,"abstract":"Abstract Bresse system over the interval (0, L ) with pointwise dissipation at $$\\xi \\in (0,{L})$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>ξ</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi>L</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> is analyzed. The exponential stability of the related semigroup is shown provided the dissipative points are of the form $$\\xi \\in \\mathbb {Q}{L}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>ξ</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>Q</mml:mi> <mml:mi>L</mml:mi> </mml:mrow> </mml:math> and $$\\xi \\ne \\frac{n}{2m+1}L$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>ξ</mml:mi> <mml:mo>≠</mml:mo> <mml:mfrac> <mml:mi>n</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>m</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:mfrac> <mml:mi>L</mml:mi> </mml:mrow> </mml:math> , where $$n,m\\in \\mathbb {N}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>,</mml:mo> <mml:mi>m</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>N</mml:mi> </mml:mrow> </mml:math> and n , and $$2m+1$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>m</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> are co-prime.","PeriodicalId":54401,"journal":{"name":"Zeitschrift fur Angewandte Mathematik und Physik","volume":"16 1","pages":"0"},"PeriodicalIF":1.7000,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Pointwise stabilization of Bresse systems\",\"authors\":\"Jaime E. Muñoz Rivera, Maria Grazia Naso\",\"doi\":\"10.1007/s00033-023-02108-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Bresse system over the interval (0, L ) with pointwise dissipation at $$\\\\xi \\\\in (0,{L})$$ <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"> <mml:mrow> <mml:mi>ξ</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi>L</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> is analyzed. The exponential stability of the related semigroup is shown provided the dissipative points are of the form $$\\\\xi \\\\in \\\\mathbb {Q}{L}$$ <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"> <mml:mrow> <mml:mi>ξ</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>Q</mml:mi> <mml:mi>L</mml:mi> </mml:mrow> </mml:math> and $$\\\\xi \\\\ne \\\\frac{n}{2m+1}L$$ <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"> <mml:mrow> <mml:mi>ξ</mml:mi> <mml:mo>≠</mml:mo> <mml:mfrac> <mml:mi>n</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>m</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:mfrac> <mml:mi>L</mml:mi> </mml:mrow> </mml:math> , where $$n,m\\\\in \\\\mathbb {N}$$ <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>,</mml:mo> <mml:mi>m</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>N</mml:mi> </mml:mrow> </mml:math> and n , and $$2m+1$$ <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>m</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> are co-prime.\",\"PeriodicalId\":54401,\"journal\":{\"name\":\"Zeitschrift fur Angewandte Mathematik und Physik\",\"volume\":\"16 1\",\"pages\":\"0\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2023-10-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Zeitschrift fur Angewandte Mathematik und Physik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s00033-023-02108-4\",\"RegionNum\":3,\"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":"Zeitschrift fur Angewandte Mathematik und Physik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00033-023-02108-4","RegionNum":3,"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

摘要分析了区间(0,L)上具有点向耗散($$\xi \in (0,{L})$$ ξ∈(0,L)的Bresse系统。给出了相关半群的指数稳定性，其耗散点为$$\xi \in \mathbb {Q}{L}$$ ξ∈Q L和$$\xi \ne \frac{n}{2m+1}L$$ ξ≠n 2 m + 1 L，其中$$n,m\in \mathbb {N}$$ n, m∈n和n, $$2m+1$$ 2 m + 1为共素数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Pointwise stabilization of Bresse systems

查看原文本刊更多论文

Pointwise stabilization of Bresse systems

Abstract Bresse system over the interval (0, L ) with pointwise dissipation at $$\xi \in (0,{L})$$ ξ ∈ ( 0 , L ) is analyzed. The exponential stability of the related semigroup is shown provided the dissipative points are of the form $$\xi \in \mathbb {Q}{L}$$ ξ ∈ Q L and $$\xi \ne \frac{n}{2m+1}L$$ ξ ≠ n 2 m + 1 L , where $$n,m\in \mathbb {N}$$ n , m ∈ N and n , and $$2m+1$$ 2 m + 1 are co-prime.

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

Zeitschrift fur Angewandte Mathematik und Physik 数学-应用数学

CiteScore

2.90

自引率

10.00%

发文量

216

审稿时长

6-12 weeks

期刊介绍： The Journal of Applied Mathematics and Physics (ZAMP) publishes papers of high scientific quality in Fluid Mechanics, Mechanics of Solids and Differential Equations/Applied Mathematics. A paper will be considered for publication if at least one of the following conditions is fulfilled: The paper includes results or discussions which can be considered original and highly interesting. The paper presents a new method. The author reviews a problem or a class of problems with such profound insight that further research is encouraged. The readers of ZAMP will find not only articles in their own special field but also original work in neighbouring domains. This will lead to an exchange of ideas; concepts and methods which have proven to be successful in one field may well be useful to other areas. ZAMP attempts to publish articles reasonably quickly. Longer papers are published in the section "Original Papers", shorter ones may appear under "Brief Reports" where publication is particularly rapid. The journal includes a "Book Review" section and provides information on activities (such as upcoming symposia, meetings or special courses) which are of interest to its readers.