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Research Article | Open Access

Nonlinear three layer beam system: Well-posedness, asymptotic stability and numerical analysis

Soh Edwin Mukiawa1( ), Cyril Dennis Enyi1,2, Johnson D. Audu3, Hasan A. Almutairi1
Department of Mathematics, College of Science, University of Hafr Al Batin, Hafr Al Batin 39524, Saudi Arabia
Mount Vernon Nazarene University, 800 Martinsburg Road Mount Vernon, OH 43050, United States of America
Department of Mathematics and Natural Sciences, Prince Mohammed Bin Fahd University Alkhobar, 31952, Saudi Arabia
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Abstract

Our goal of this work is to study the well-posedness and the asymptotic behavior of solutions of a nonlinear triple beam system commonly known as the Rao-Nakra beam model. We investigated the effects of non-linear frictional and external forces to the beam model. The Garlekin approximation and the multiplier methods were techniques applied to achieve our goals. Numerical approximations were also performed with the finite difference method to validate our theoritical findings.

Keywords

well-posednesspolynomial and exponential stabilitynumerical approximationnonlinear Rao-Nakra beam
CLC number: 35D30, 35B35, 35L51, 74J30, 74S20

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AIMS Mathematics
Volume 10 Issue 10,
October 2025
Pages 24389-24430
DOI: 10.3934/math.20251082

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Mukiawa SE, Enyi CD, Audu JD, et al. Nonlinear three layer beam system: Well-posedness, asymptotic stability and numerical analysis. AIMS Mathematics, 2025, 10(10): 24389-24430. https://doi.org/10.3934/math.20251082

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Received: 26 July 2025
Revised: 12 October 2025
Accepted: 16 October 2025
Published: 24 October 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)