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Article

A New Perspective on the Energy Decay of the Timoshenko–Ehrenfest System: The Non-Local Truncated Approach

by
Hamza Zougheib
1,
Toufic El Arwadi
1 and
Toni Sayah
2,*
1
Department of Mathematics and Computer Science, Faculty of Science, Beirut Arab University, B.P. 11-5020, Riald El Solh, Beirut 1107 2809, Lebanon
2
Laboratoire de Mathétiques et Applications, Unité de recherche Mathématiques et Modélisation, CAR, Faculté des Sciences, Université Saint-Joseph, B.P. 11-514 Riad El Solh, Beirut 1107 2050, Lebanon
*
Author to whom correspondence should be addressed.
Mathematics 2026, 14(7), 1132; https://doi.org/10.3390/math14071132
Submission received: 4 February 2026 / Revised: 11 March 2026 / Accepted: 17 March 2026 / Published: 28 March 2026
(This article belongs to the Special Issue Mathematical Optimization and Control: Methods and Applications, 2nd Edition)
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Abstract

This paper presents a new perspective on the energy decay of a nonlocal truncated Timoshenko–Ehrenfest system. By using the non local elasticity theory, this model is a generalization of the standard truncated Timoshenko system. The well-posedness of the proposed model is established via the Faedo-Galerkin method. Energy stability and decay properties are then derived using suitable multiplier techniques. Finally, a numerical scheme is constructed, and the exponential decay of the discrete energy is given special attention. Numerical simulations are provided to illustrate and validate the theoretical results.
Keywords: Timoshenko–Ehrenfest; energy decay; truncated approach; finite element method Timoshenko–Ehrenfest; energy decay; truncated approach; finite element method

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MDPI and ACS Style

Zougheib, H.; El Arwadi, T.; Sayah, T. A New Perspective on the Energy Decay of the Timoshenko–Ehrenfest System: The Non-Local Truncated Approach. Mathematics 2026, 14, 1132. https://doi.org/10.3390/math14071132

AMA Style

Zougheib H, El Arwadi T, Sayah T. A New Perspective on the Energy Decay of the Timoshenko–Ehrenfest System: The Non-Local Truncated Approach. Mathematics. 2026; 14(7):1132. https://doi.org/10.3390/math14071132

Chicago/Turabian Style

Zougheib, Hamza, Toufic El Arwadi, and Toni Sayah. 2026. "A New Perspective on the Energy Decay of the Timoshenko–Ehrenfest System: The Non-Local Truncated Approach" Mathematics 14, no. 7: 1132. https://doi.org/10.3390/math14071132

APA Style

Zougheib, H., El Arwadi, T., & Sayah, T. (2026). A New Perspective on the Energy Decay of the Timoshenko–Ehrenfest System: The Non-Local Truncated Approach. Mathematics, 14(7), 1132. https://doi.org/10.3390/math14071132

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