{"title":"Decay property for a novel partially dissipative viscoelastic beam system on the real line","authors":"N. Mori, M. A. Jorge Silva","doi":"10.1142/s0219891622500114","DOIUrl":null,"url":null,"abstract":"We address here a viscoelastic Timoshenko model on the (one-dimensional) real line with memory damping coupled on a shear force. Our main results concern a complete decay structure of the system under the so-called equal wave speeds assumption, as well as without this condition. This is the first result of this type for partially dissipative beam systems with memory-type damping on the shear force. Our method is based on expanded structural conditions such as the so-called SK condition. In addition, we give a characterization of the dissipative structure of the system by using a spectral analysis method, which confirms that our decay structure is optimal.","PeriodicalId":50182,"journal":{"name":"Journal of Hyperbolic Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Hyperbolic Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0219891622500114","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 1
Abstract
We address here a viscoelastic Timoshenko model on the (one-dimensional) real line with memory damping coupled on a shear force. Our main results concern a complete decay structure of the system under the so-called equal wave speeds assumption, as well as without this condition. This is the first result of this type for partially dissipative beam systems with memory-type damping on the shear force. Our method is based on expanded structural conditions such as the so-called SK condition. In addition, we give a characterization of the dissipative structure of the system by using a spectral analysis method, which confirms that our decay structure is optimal.
期刊介绍：
This journal publishes original research papers on nonlinear hyperbolic problems and related topics, of mathematical and/or physical interest. Specifically, it invites papers on the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising in mathematical physics. The Journal welcomes contributions in:
Theory of nonlinear hyperbolic systems of conservation laws, addressing the issues of well-posedness and qualitative behavior of solutions, in one or several space dimensions.
Hyperbolic differential equations of mathematical physics, such as the Einstein equations of general relativity, Dirac equations, Maxwell equations, relativistic fluid models, etc.
Lorentzian geometry, particularly global geometric and causal theoretic aspects of spacetimes satisfying the Einstein equations.
Nonlinear hyperbolic systems arising in continuum physics such as: hyperbolic models of fluid dynamics, mixed models of transonic flows, etc.
General problems that are dominated (but not exclusively driven) by finite speed phenomena, such as dissipative and dispersive perturbations of hyperbolic systems, and models from statistical mechanics and other probabilistic models relevant to the derivation of fluid dynamical equations.
Convergence analysis of numerical methods for hyperbolic equations: finite difference schemes, finite volumes schemes, etc.
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