Uniform stability of a thermodiffusion Timoshenko beam

Fayssal Djellali (), Tijani A. Apalara () and Mohamed Zitouni ()
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Fayssal Djellali: Badji-Mokhtar University
Tijani A. Apalara: University of Hafr Al-Batin (UHB)
Mohamed Zitouni: Badji-Mokhtar University

Partial Differential Equations and Applications, 2023, vol. 4, issue 3, 1-20

Abstract: Abstract The main object of the present work is the study of a new Timoshenko beam model with thermal and mass diffusion effects where the coupling is acting on the shear force. We prove the well-posedness of the system using the semigroup theory. Furthermore, we establish that the system is exponentially stable if and only if the wave speeds of the system are equal. When the speeds of the mechanical waves are different, we show a lack of exponential stability. Additionally, in the case of different wave speeds, we show that the solution decays polynomially.

Keywords: Timoshenko beam; Thermodiffusion effects; Stability; Lack of exponential stability; 35B40; 47D03; 74F05; 74K10; 93D20 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s42985-023-00243-1

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