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arXiv · 1512.08006

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

Ahmed Bchatnia·Makram Hamouda·Mohamed Ali Ayadi
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Abstract

In this work, we consider a nonlinear vibrating Timoshenko system with thermoelasticity with second sound. We recall first the results of well-posdness and regularity and the asymptotic behavior of the energy obtained in \cite{Ayadi}. Then, we use a fourth order finite difference scheme to compute the numerical solutions and thus we show the energy decay in several cases depending on the stability number. Résumé : Dans ce travail, on considère le système de Timoshenko non-linéaire avec Thermo-élasticité et deuxième son. On rappelle d'abord les résultats d'existence, de régularité et du comportement asymptotique de l'énergie obtenus dans \cite{Ayadi}. Ensuite, on valide numériquement ces résultats théoriques. Pour cela, on utilise une méthode de différences finies d'ordre $4$. Ainsi la solution numérique obtenue permet de valider la décroissance de l'énergie dans plusieurs cas selon la valeur du paramètre de stabilité.

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Ahmed Bchatnia, Makram Hamouda, Mohamed Ali Ayadi. 2015-12-25. Numerical solutions for a Timoshenko-type system with thermoelasticity with second sound. https://arxiv.org/abs/1512.08006

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