Numerical solutions for a Timoshenko-type system with thermoelasticity with second sound

Makram Hamouda; Ahmed Bchatnia; Mohamed Ali Ayadi

doi:10.3934/dcdss.2021001

Article Contents

2021, Volume 14, Issue 8: 2975-2992. Doi: 10.3934/dcdss.2021001

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Numerical solutions for a Timoshenko-type system with thermoelasticity with second sound

1.
Department of Basic Sciences, Deanship of Preparatory Year and Supporting Studies, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam 34212, Saudi Arabia
2.
UR ANALYSE NON-LINÉAIRE ET GÉOMETRIE, UR13ES32 Department of Mathematics, Faculty of Sciences of Tunis, University of Tunis El-Manar 2092 El Manar II, Tunisia
3.
UR ANALYSE NON-LINÉAIRE ET GÉOMETRIE, UR13ES32 ESPRIT School of Engineering. 1, 2 rue André Ampère 2083 - Pôle Technologique, El Ghazala

^* Corresponding author: Makram Hamouda
^* Corresponding author: Makram Hamouda

Dedicated to the memory of Professor Ezzedine Zahrouni

Received: May 31, 2020

Revised: October 31, 2020

Early access: January 2021

Published: August 2021

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Abstract

We consider in this article a nonlinear vibrating Timoshenko system with thermoelasticity with second sound. We first recall the results obtained in [2] concerning the well-posedness, the regularity of the solutions and the asymptotic behavior of the associated energy. Then, we use a fourth-order finite difference scheme to compute the numerical solutions and we prove its convergence. The energy decay in several cases, depending on the stability number $ \mu $, are numerically and theoretically studied.

Keywords:

Asymptotic behavior of solutions,
asymptotic stability,
finite difference methods,
stability and convergence of numerical methods,
thermoelasticity,
Timoshenko system.

Mathematics Subject Classification: Primary:65M06, 65L20, 35B35, 35B40, 93D20.

Citation:

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Figure 1. Mesh of the domain $ \Omega_{h} \times T_{n} $

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Figure 2.

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