The influence of damping on the asymptotic behavior of solution for laminated beam

Abdelkader Moumen; Fares Yazid; Fatima Siham Djeradi; Moheddine Imsatfia; Tayeb Mahrouz; Keltoum Bouhali; Abdelkader Moumen; Fares Yazid; Fatima Siham Djeradi; Moheddine Imsatfia; Tayeb Mahrouz; Keltoum Bouhali

doi:10.3934/math.20241101

AIMS Mathematics

2024, Volume 9, Issue 8: 22602-22626. doi: 10.3934/math.20241101

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The influence of damping on the asymptotic behavior of solution for laminated beam

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 55473, Saudi Arabia; Email: mo.abdelkader@uoh.edu.sa
2.
Laboratory of pure and applied mathematics, University of Amar Telidji, Laghouat, Algeria; Email: f.yazid@lagh-univ.dz (F.Y.), fs.djeradi@lagh-univ.dz (F.S.D.)
3.
Mathematics Department, Faculty of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia; Email: mblgasim@kku.edu.sa
4.
Department of Mathematics, Faculty of Sciences, University of Ibn Khladoun, BP P 78 Zaaroura, Tiaret 14000, Algeria; Email: tayeb.mahrouz@univ-tiaret.dz
5.
Department of Mathematics, College of Science, Qassim University, Saudi Arabia; Email: k.bouhali@qu.edu.sa

Received: 22 April 2024 Revised: 11 July 2024 Accepted: 15 July 2024 Published: 22 July 2024
MSC : 35B40, 35L56, 93D15

This paper dealt with a laminated beam system along with structural damping, past history, distributed delay, and in the presence of both temperatures and micro-temperatures effects. The damping terms left the system dissipative. Employing the semigroup approach, we established the existence and uniqueness of the solution. Additionally, with the help of convenient assumptions on the kernel, we demonstrated a general decay result for the solution of the considered system, with no constraints regarding the speeds of wave propagation. The main aim was to address how specific behaviors of the system were related to memory and delays. We aimed to investigate the joint impact of an infinite memory, distributed delay and micro-temperature effects on the system. We found a new relationship between the decay rate of solution and the growth of g at infinity. The objective was to find studies that use no- trivial results and their applications to relevant problems from mathematical physics.
- laminated beam,
- stability,
- well-posedness,
- micro-temperature effects,
- structural damping,
- Lyapunov functions,
- distributed delay,
- past history,
- dynamical systems
Citation: Abdelkader Moumen, Fares Yazid, Fatima Siham Djeradi, Moheddine Imsatfia, Tayeb Mahrouz, Keltoum Bouhali. The influence of damping on the asymptotic behavior of solution for laminated beam[J]. AIMS Mathematics, 2024, 9(8): 22602-22626. doi: 10.3934/math.20241101

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Abstract

This paper dealt with a laminated beam system along with structural damping, past history, distributed delay, and in the presence of both temperatures and micro-temperatures effects. The damping terms left the system dissipative. Employing the semigroup approach, we established the existence and uniqueness of the solution. Additionally, with the help of convenient assumptions on the kernel, we demonstrated a general decay result for the solution of the considered system, with no constraints regarding the speeds of wave propagation. The main aim was to address how specific behaviors of the system were related to memory and delays. We aimed to investigate the joint impact of an infinite memory, distributed delay and micro-temperature effects on the system. We found a new relationship between the decay rate of solution and the growth of g at infinity. The objective was to find studies that use no- trivial results and their applications to relevant problems from mathematical physics.

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