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Research Article | Open Access

On the exponential decay of a Balakrishnan-Taylor plate with strong damping

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

In this manuscript, we study a thin and narrow plate equation that models the deck of a suspension bridge that is subject to a Balakrishnan-Taylor damping and a strong damping. First, by using the Faedo Galerkin method, we prove the existence of both global weak and regular solutions. Second, we prove the exponential stability of the energy for regular solutions by combining the multiplier method and a well-known result of Komornik.

Keywords

plateBalakrishnan-Taylor dampingstrong dampingexponential decay
CLC number: 35B40, 35L75, 74K10

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AIMS Mathematics
Volume 9 Issue 6,
May 2024
Pages 14026-14042
DOI: 10.3934/math.2024682

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Cite this article:
Hajjej Z. On the exponential decay of a Balakrishnan-Taylor plate with strong damping. AIMS Mathematics, 2024, 9(6): 14026-14042. https://doi.org/10.3934/math.2024682

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Received: 03 January 2024
Revised: 30 March 2024
Accepted: 08 April 2024
Published: 18 April 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)