| Issue |
ESAIM: M2AN
Volume 57, Number 3, May-June 2023
|
|
|---|---|---|
| Page(s) | 1171 - 1193 | |
| DOI | https://doi.org/10.1051/m2an/2023002 | |
| Published online | 08 May 2023 | |
Exponential stabilization for carbon nanotubes modeled as Timoshenko beams with thermoelastic effects
1
Faculty of Mathematics, Federal University of Pará, Salinópolis, PA, Brazil
2
Institute of Computing, Federal University of Rio de Janeiro, RJ, Brazil
* Corresponding author: ramos@ufpa.br
Received:
17
May
2022
Accepted:
30
December
2022
In this article we consider the problem of heat conduction in carbon nanotubes modeled like Timoshenko beams, inspired by the work of Yoon et al. [Compos. Part B: Eng. 35 (2004) 87–93]. 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.
Mathematics Subject Classification: 93D22 / 65M06 / 65M15
Key words: Carbon nanotubes / exponential stability / numerical analysis / numerical simulation / convergence order
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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