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Research Article | Open Access

A suspension bridges with a fractional time delay: Asymptotic behavior and Blow-up in finite time

Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
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Abstract

In the present paper, we examine a suspension bridges model subject to frictional damping, a fractional delay term, and a source term. First, we prove the existence of global solutions of the problem. Second, for small initial data, we establish the exponential stability of the system by using the energy method. Additionally, we show that if the initial energy assumes a negative value, the solution blows up in finite time.

Keywords

suspension bridgesfractional delayexponential stabilityblow-up
CLC number: 26A33, 35B44, 74K20, 93D23

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AIMS Mathematics
Volume 9 Issue 8,
August 2024
Pages 22022-22040
DOI: 10.3934/math.20241070

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Cite this article:
Hajjej Z. A suspension bridges with a fractional time delay: Asymptotic behavior and Blow-up in finite time. AIMS Mathematics, 2024, 9(8): 22022-22040. https://doi.org/10.3934/math.20241070

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Received: 04 June 2024
Revised: 04 July 2024
Accepted: 08 July 2024
Published: 15 August 2024
©2024 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)