两个耗散光束之间接触问题的存在性和指数衰减

IF 1.8 3区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY

Journal of Elasticity Pub Date : 2024-04-03 DOI:10.1007/s10659-024-10064-x

{"title":"两个耗散光束之间接触问题的存在性和指数衰减","authors":"","doi":"10.1007/s10659-024-10064-x","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>We deal with the Signorini contact problem between two Timoshenko beams. In this work we use the theory of semigroups to show the existence of solutions that decay uniformly to zero. This method is new and more effective than the widely used energy method. This is because in particular we obtain uniform decay of the solutions to zero for any boundary condition. A second important point is that we can take advantage of stabilization results of others linear dynamic systems with different dissipative mechanisms and apply them through our method for Contact Problems (see Sect. <span>4</span>). Finally, thanks to Lipschitzian perturbations we can generalize the Signorini problem to more general semi linear problems in a simple way (see Sect. <span>4.3</span>).</p>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Existence and Exponential Decay for a Contact Problem Between Two Dissipative Beams\",\"authors\":\"\",\"doi\":\"10.1007/s10659-024-10064-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3>Abstract</h3> <p>We deal with the Signorini contact problem between two Timoshenko beams. In this work we use the theory of semigroups to show the existence of solutions that decay uniformly to zero. This method is new and more effective than the widely used energy method. This is because in particular we obtain uniform decay of the solutions to zero for any boundary condition. A second important point is that we can take advantage of stabilization results of others linear dynamic systems with different dissipative mechanisms and apply them through our method for Contact Problems (see Sect. <span>4</span>). Finally, thanks to Lipschitzian perturbations we can generalize the Signorini problem to more general semi linear problems in a simple way (see Sect. <span>4.3</span>).</p>\",\"PeriodicalId\":624,\"journal\":{\"name\":\"Journal of Elasticity\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2024-04-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Elasticity\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1007/s10659-024-10064-x\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Elasticity","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1007/s10659-024-10064-x","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

摘要

摘要我们讨论了两个季莫申科梁之间的西格诺里尼接触问题。在这项工作中，我们利用半群理论证明了均匀衰减为零的解的存在性。这种方法是一种新方法，比广泛使用的能量法更有效。这是因为我们可以在任何边界条件下获得均匀衰减为零的解。第二个要点是，我们可以利用其他具有不同耗散机制的线性动力系统的稳定结果，并通过我们的方法将其应用于接触问题（见第 4 节）。最后，得益于 Lipschitzian perturbations，我们可以用一种简单的方法将 Signorini 问题推广到更一般的半线性问题中（见第 4.3 节）。

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

Existence and Exponential Decay for a Contact Problem Between Two Dissipative Beams

Abstract

We deal with the Signorini contact problem between two Timoshenko beams. In this work we use the theory of semigroups to show the existence of solutions that decay uniformly to zero. This method is new and more effective than the widely used energy method. This is because in particular we obtain uniform decay of the solutions to zero for any boundary condition. A second important point is that we can take advantage of stabilization results of others linear dynamic systems with different dissipative mechanisms and apply them through our method for Contact Problems (see Sect. 4). Finally, thanks to Lipschitzian perturbations we can generalize the Signorini problem to more general semi linear problems in a simple way (see Sect. 4.3).

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

Journal of Elasticity 工程技术-材料科学：综合

CiteScore

3.70

自引率

15.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Elasticity was founded in 1971 by Marvin Stippes (1922-1979), with its main purpose being to report original and significant discoveries in elasticity. The Journal has broadened in scope over the years to include original contributions in the physical and mathematical science of solids. The areas of rational mechanics, mechanics of materials, including theories of soft materials, biomechanics, and engineering sciences that contribute to fundamental advancements in understanding and predicting the complex behavior of solids are particularly welcomed. The role of elasticity in all such behavior is well recognized and reporting significant discoveries in elasticity remains important to the Journal, as is its relation to thermal and mass transport, electromagnetism, and chemical reactions. Fundamental research that applies the concepts of physics and elements of applied mathematical science is of particular interest. Original research contributions will appear as either full research papers or research notes. Well-documented historical essays and reviews also are welcomed. Materials that will prove effective in teaching will appear as classroom notes. Computational and/or experimental investigations that emphasize relationships to the modeling of the novel physical behavior of solids at all scales are of interest. Guidance principles for content are to be found in the current interests of the Editorial Board.