Stability rate of a thermoelastic laminated beam: Case of equal-wave speed and nonequal-wave speed of propagation

Soh E. Mukiawa; Tijani A. Apalara; Salim A. Messaoudi; Soh E. Mukiawa; Tijani A. Apalara; Salim A. Messaoudi

doi:10.3934/math.2021021

AIMS Mathematics

2021, Volume 6, Issue 1: 333-361. doi: 10.3934/math.2021021

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Research article

Stability rate of a thermoelastic laminated beam: Case of equal-wave speed and nonequal-wave speed of propagation

1.
Department of Mathematics, University of Hafr Al Batin, Hafr Al Batin 31991, Saudi Arabia
2.
Department of Mathematics and Statistics University of Sharjah Sharjah, United Arab Emirates
3.
Department of Mathematics and Statistics, KFUPM, Dhahran 31261, Saudi Arabia

Received: 14 July 2020 Accepted: 23 September 2020 Published: 12 October 2020
MSC : 35D30, 35D35, 35B35, 35L51, 74D10, 93D15

In this article, we investigate a one-dimensional thermoelastic laminated beam system with viscoelastic dissipation on the effective rotation angle and through heat conduction in the interfacial slip equations. Under general conditions on the relaxation function and the relationship between the coefficients of the wave propagation speed of the first two equations, we show that the solution energy has an explicit and general decay rate from which the exponential and polynomial stability are just particular cases. Moreover, we establish a weaker decay result in the case of non-equal wave of speed propagation and give some examples to illustrate our results. This new result improves substantially many other results in the literature.
- general decay,
- Laminated beam,
- thermoelasticitty,
- fourier heat conduction,
- viscoelasticity,
- convexity,
- optimal
Citation: Soh E. Mukiawa, Tijani A. Apalara, Salim A. Messaoudi. Stability rate of a thermoelastic laminated beam: Case of equal-wave speed and nonequal-wave speed of propagation[J]. AIMS Mathematics, 2021, 6(1): 333-361. doi: 10.3934/math.2021021

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Abstract

In this article, we investigate a one-dimensional thermoelastic laminated beam system with viscoelastic dissipation on the effective rotation angle and through heat conduction in the interfacial slip equations. Under general conditions on the relaxation function and the relationship between the coefficients of the wave propagation speed of the first two equations, we show that the solution energy has an explicit and general decay rate from which the exponential and polynomial stability are just particular cases. Moreover, we establish a weaker decay result in the case of non-equal wave of speed propagation and give some examples to illustrate our results. This new result improves substantially many other results in the literature.

References

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