Well-posedness and stabilization of a type three layer beam system with Gurtin-Pipkin's thermal law

Soh Edwin Mukiawa; Soh Edwin Mukiawa

doi:10.3934/math.20231443

AIMS Mathematics

2023, Volume 8, Issue 12: 28188-28209. doi: 10.3934/math.20231443

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Well-posedness and stabilization of a type three layer beam system with Gurtin-Pipkin's thermal law

Soh Edwin Mukiawa ^,

Department of Mathematics, University of Hafr Al Batin, Hafr Al Batin 31991, Saudi Arabia

Received: 14 June 2023 Revised: 03 September 2023 Accepted: 08 October 2023 Published: 13 October 2023
MSC : 35B35, 35B40, 35D30, 35D35, 93D20

The goal of this work is to study the well-posedness and the asymptotic behavior of solutions of a triple beam system commonly known as the Rao-Nakra beam model. We consider the effect of Gurtin-Pipkin's thermal law on the outer layers of the beam system. Using standard semi-group theory for linear operators and the multiplier method, we establish the existence and uniqueness of weak global solution, as well as a stability result.
- Rao-Nakra,
- triple-layer beam beam,
- Gurtin-Pipkin conduction,
- well-posedness,
- stability analysis
Citation: Soh Edwin Mukiawa. Well-posedness and stabilization of a type three layer beam system with Gurtin-Pipkin's thermal law[J]. AIMS Mathematics, 2023, 8(12): 28188-28209. doi: 10.3934/math.20231443

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Abstract

The goal of this work is to study the well-posedness and the asymptotic behavior of solutions of a triple beam system commonly known as the Rao-Nakra beam model. We consider the effect of Gurtin-Pipkin's thermal law on the outer layers of the beam system. Using standard semi-group theory for linear operators and the multiplier method, we establish the existence and uniqueness of weak global solution, as well as a stability result.

References

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