ON THE EXISTENCE AND STABILITY OF SOLUTIONS OF A TYPE-III THERMOELASTIC TRUNCATED TIMOSHENKO SYSTEM

Afaf Ahmima; Salim A. Messaoudi; Mohamed Alahyane

doi:10.11948/20240019

2024 Volume 14 Issue 6

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Afaf Ahmima, Salim A. Messaoudi, Mohamed Alahyane. ON THE EXISTENCE AND STABILITY OF SOLUTIONS OF A TYPE-III THERMOELASTIC TRUNCATED TIMOSHENKO SYSTEM[J]. Journal of Applied Analysis & Computation, 2024, 14(6): 3385-3403. doi: 10.11948/20240019

Citation:

Afaf Ahmima, Salim A. Messaoudi, Mohamed Alahyane. ON THE EXISTENCE AND STABILITY OF SOLUTIONS OF A TYPE-III THERMOELASTIC TRUNCATED TIMOSHENKO SYSTEM[J]. Journal of Applied Analysis & Computation, 2024, 14(6): 3385-3403. doi: 10.11948/20240019

ON THE EXISTENCE AND STABILITY OF SOLUTIONS OF A TYPE-III THERMOELASTIC TRUNCATED TIMOSHENKO SYSTEM

1.
Laboratory of operators theory and PDEs, University of El Oued, Faculty of exact sciences, P.O.B. 789, 39000 El Oued, Algeria
2.
Department of Mathematics, College of Sciences, University of Sharjah, Sharjah, UAE
3.
MIA Laboratory, La Rochelle University, 17000 La Rochelle, France

Author Bio: Email: afafahmima@gmail.com(A. Ahmima); Email: smessaoudi@sharjah.ac.ae(S. Messaoudi)
Corresponding author: Email: mohamed.alahyane@univ-lr.fr(M. Alahyane)

Abstract

Abstract

This paper is concerned with the well-posedness and stability of a one-dimensional thermoelastic truncated Timoshenko system of Type III. In order to establish the well-posedness, we first solve an auxiliary problem and give the proof in details, using the semigroup theory and some non traditional operators. Then, we use this result to solve our original problem. After that, we prove that the presence of the thermal effect in one equation only is strong enough to drive the system exponentially to rest, irrespective to any relation between the coefficients. By the end of the work, we present some numerical tests to illustrate our theoretical findings.
- Exponential decay /
- Timoshenko /
- thermoelasticity type III /
- well-posedness /
- truncated
MSC: 35B37, 35L55, 74D05, 93D15, 93D20

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References

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