{"title":"Controllability of a thermoelastic system","authors":"F. D. Araruna, A. Mercado, Luz de Teresa","doi":"10.3233/asy-221815","DOIUrl":null,"url":null,"abstract":"In this paper we present a null controllability result for a thermoelastic Rayleigh system. Instead of working directly with the control system, we obtain the controlled system as the modulus of elasticity in shear tends to infinity in the corresponding thermoelastic Mindlin–Timoshenko system. Our results follow the seminal book of Lagnese and Lions (Rech. Math. Appl. 6(1988)) where the controllability of a Kirkhhoff model is proposed as the limit of a controlled Mindlin–Timoshenko one. We use estimates for some eigenvalues of the beam model that were obtained in (SIAM J. Control Optim. 47 (2008) 1909–1938) and the recent paper of Komornik and Tenenbaum (Evolution Equations and Control Theory 4(3) (2015) 297–314) where explicit estimates for systems with real and complex eigenvalues are proposed.","PeriodicalId":55438,"journal":{"name":"Asymptotic Analysis","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2022-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asymptotic Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3233/asy-221815","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
Abstract
In this paper we present a null controllability result for a thermoelastic Rayleigh system. Instead of working directly with the control system, we obtain the controlled system as the modulus of elasticity in shear tends to infinity in the corresponding thermoelastic Mindlin–Timoshenko system. Our results follow the seminal book of Lagnese and Lions (Rech. Math. Appl. 6(1988)) where the controllability of a Kirkhhoff model is proposed as the limit of a controlled Mindlin–Timoshenko one. We use estimates for some eigenvalues of the beam model that were obtained in (SIAM J. Control Optim. 47 (2008) 1909–1938) and the recent paper of Komornik and Tenenbaum (Evolution Equations and Control Theory 4(3) (2015) 297–314) where explicit estimates for systems with real and complex eigenvalues are proposed.
本文给出了热弹性瑞利系统的零可控性结果。而不是直接与控制系统工作，我们得到控制系统的剪切弹性模量趋于无穷大，在相应的热弹性Mindlin-Timoshenko系统。我们的研究结果遵循了影响深远的《拉格内斯与狮子》一书。数学。其中Kirkhhoff模型的可控性被提出为受控Mindlin-Timoshenko模型的极限。我们使用了在(SIAM J. Control Optim. 47(2008) 1909-1938)和Komornik和Tenenbaum最近的论文(进化方程和控制理论4(3)(2015)297-314)中获得的梁模型的一些特征值的估计，其中提出了对具有实特征值和复数特征值的系统的显式估计。
期刊介绍：
The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand. Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.
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