Exponential stabilization for carbon nanotubes modeled as Timoshenko beams with thermoelastic effects

IF 1.9 3区 数学 Q2 Mathematics
Anderson de Jesus Araújo Ramos, M. Rincon, Rodrigo L. R. Madureira, M. Freitas
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引用次数: 1

Abstract

In this article we consider the problem of heat conduction in carbon nanotubes modeled like Timoshenko beams, inspired by the work of J. Yoon \textit{et al.} (Composites Part B: Engineering, \textbf{35}(2), 87--93. 2004). Using the theory of semigroups of linear operators, we prove the well-posedness of the problem and the exponential stabilization of the total energy of the system of differential equations, partially damped, without assuming the known relationship of equality of wave velocities. Furthermore, we analyze the fully discrete problem using a finite difference scheme, introduced by a spatiotemporal discretization that combines explicit and implicit integration methods. We show the construction of numerical energy and simulations that prove our theoretical exponential decay results and display the convergence rates.
具有热弹性效应的Timoshenko光束型碳纳米管的指数稳定性
在这篇文章中,我们考虑了像Timoshenko光束一样的碳纳米管的热传导问题,灵感来自J. Yoon\textit{等人}的工作(复合材料B部分:工程,\textbf{35}(2),87—93)。2004)。利用线性算子的半群理论,在不假设已知波速相等关系的情况下,证明了问题的适定性和部分阻尼微分方程组总能量的指数镇定性。此外,我们使用有限差分格式分析完全离散问题,该格式由结合显式和隐式积分方法的时空离散化引入。我们展示了数值能量的构造和模拟,证明了我们的理论指数衰减结果并显示了收敛速度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
2.70
自引率
5.30%
发文量
27
审稿时长
6-12 weeks
期刊介绍: M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.
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