On the internal and boundary stabilization of a nonlinear suspension bridge system: Exponential and polynomial decay rates

Ahmad Mugbil; Mohammad M. Al-Gharabli; Adel M. Al-Mahdi; Abdelaziz Soufyane

doi:10.3934/eect.2024022

Article Contents

2024, Volume 13, Issue 4: 1199-1211. Doi: 10.3934/eect.2024022

This issue Previous Article Existence of strong solutions for a compressible fluid-solid interaction system with Navier slip boundary conditions Next Article Approximation of the set of integrable trajectories of the control system with $ L_2 $ norm constraints on control functions

On the internal and boundary stabilization of a nonlinear suspension bridge system: Exponential and polynomial decay rates

1.
The Preparatory Year Program, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
2.
Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
3.
The (IRC) in Construction and Building Materials, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
4.
Department of Mathematics, College of Science, University of Sharjah, P. O. Box 27272, Sharjah, United Arab Emirates

^*Corresponding author: Adel M. Al-Mahdi
^*Corresponding author: Adel M. Al-Mahdi

Received: November 2023

Revised: March 2024

Early access: April 8, 2024

Published online: April 8, 2024

The second and third authors are supported by KFUPM[Grant No. INCB2404].

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Abstract

In this paper, we study the asymptotic behavior of solutions for unconstrained one dimensional suspension bridge model. We dissipate the system with two nonlinear dampings of variable exponents-type. We obtain exponential and polynomial decay results based on the range of the variable exponents by using the multiplier method. Our results built on, developed and generalized some earlier results in the literature.

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Mathematics Subject Classification: Primary: 35B37, 35B40, 74D99; Secondary: 93D15; 93D20.

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