Summer 2021 New general decay result of the laminated beam system with infinite history
Adel M. Al-Mahdi, Mohammad M. Al-Gharabli, Salim A. Messaoudi
J. Integral Equations Applications 33(2): 137-154 (Summer 2021). DOI: 10.1216/jie.2021.33.137


This paper is concerned with the asymptotic behavior of the solution of a laminated Timoshenko beam system with viscoelastic damping. We extend the work known for this system with finite memory to the case of infinite memory. We use minimal and general conditions on the relaxation function and establish explicit energy decay formula, which gives the best decay rates expected under this level of generality. We assume that the relaxation function g satisfies, for some nonnegative functions ξ and H, g(t)ξ(t)H(g(t)), t0. Our decay results generalize and improve many earlier results in the literature. Moreover, we remove some assumptions on the boundedness of initial data used in many earlier papers in the literature.


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Adel M. Al-Mahdi. Mohammad M. Al-Gharabli. Salim A. Messaoudi. "New general decay result of the laminated beam system with infinite history." J. Integral Equations Applications 33 (2) 137 - 154, Summer 2021.


Received: 19 March 2020; Revised: 14 June 2020; Accepted: 5 August 2020; Published: Summer 2021
First available in Project Euclid: 31 August 2021

MathSciNet: MR4306867
zbMATH: 1472.35044
Digital Object Identifier: 10.1216/jie.2021.33.137

Primary: 35B40 , 74F05 , 93C20 , 93D15 , 93D20

Keywords: general decay , laminated beam system , relaxation function , viscoelasticity.

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium


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Vol.33 • No. 2 • Summer 2021
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