General Decay Rates for a Laminated Beam with Memory

In previous work [23], Mustafa considered a viscoelastic laminated beam system with structural damping in the case of equal-speed wave propagations, and established explicit energy decay formula which gives the best decay rates. In this paper, we continue to consider the similar problems and establi...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 23; no. 5; pp. 1227 - 1252
Main Authors Chen, Zhijing, Liu, Wenjun, Chen, Dongqin
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.10.2019
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Summary:In previous work [23], Mustafa considered a viscoelastic laminated beam system with structural damping in the case of equal-speed wave propagations, and established explicit energy decay formula which gives the best decay rates. In this paper, we continue to consider the similar problems and establish the general decay result for the energy, to system with structural damping in the case of non-equal wave speeds and to system without structural damping in the case of equal wave speeds, respectively. For the first case, we use the second-order energy method to overcome the difficulty of estimating the non-equal speeds term. For the second case, we construct an appropriated perturbed functional to estimate w t 2 2 so as to overcome the absence of structural damping.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm/181109