Decay for thermoelastic laminated beam with nonlinear delay and nonlinear structural damping

Hicham Saber; Fares Yazid; Fatima Siham Djeradi; Mohamed Bouye; Khaled Zennir; Hicham Saber; Fares Yazid; Fatima Siham Djeradi; Mohamed Bouye; Khaled Zennir

doi:10.3934/math.2024337

AIMS Mathematics

2024, Volume 9, Issue 3: 6916-6932. doi: 10.3934/math.2024337

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Research article

Decay for thermoelastic laminated beam with nonlinear delay and nonlinear structural damping

1.
Department of Mathematics, College of Sciences, University of Ha'il, Ha'il 55473, Saudi Arabia
2.
Laboratory of pure and applied Mathematics, Amar Teledji University, Laghouat 03000, Algeria
3.
Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
4.
Department of Mathematics, College of Science, Qassim University, Saudi Arabia
5.
Department of Mathematics, Faculty of Sciences, University of 20 Août 1955- Skikda, Algeria

Received: 10 December 2023 Revised: 29 January 2024 Accepted: 08 February 2024 Published: 19 February 2024
MSC : 35B40, 35L56, 74F05, 93D15, 93D20

This paper discussed the decay of a thermoelastic laminated beam subjected to nonlinear delay and nonlinear structural damping. We provided explicit and general energy decay rates of the solution by imposing suitable conditions on both weight delay and wave speeds. To achieve this, we leveraged the properties of convex functions and employed the multiplier technique as a specific approach to demonstrate our stability results.
- Laminated beam,
- Lyapunov functions,
- nonlinear damping,
- general decay,
- nonlinear delay,
- partial differential equations
Citation: Hicham Saber, Fares Yazid, Fatima Siham Djeradi, Mohamed Bouye, Khaled Zennir. Decay for thermoelastic laminated beam with nonlinear delay and nonlinear structural damping[J]. AIMS Mathematics, 2024, 9(3): 6916-6932. doi: 10.3934/math.2024337

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Abstract

This paper discussed the decay of a thermoelastic laminated beam subjected to nonlinear delay and nonlinear structural damping. We provided explicit and general energy decay rates of the solution by imposing suitable conditions on both weight delay and wave speeds. To achieve this, we leveraged the properties of convex functions and employed the multiplier technique as a specific approach to demonstrate our stability results.

References

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