## Taiwanese Journal of Mathematics

### General Decay Rates for a Laminated Beam with Memory

This article is in its final form and can be cited using the date of online publication and the DOI.

#### Abstract

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.

#### Article information

Source
Taiwanese J. Math., Advance publication (2019), 26 pages.

Dates
First available in Project Euclid: 22 November 2018

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1542855636

Digital Object Identifier
doi:10.11650/tjm/181109

#### Citation

Chen, Zhijing; Liu, Wenjun; Chen, Dongqin. General Decay Rates for a Laminated Beam with Memory. Taiwanese J. Math., advance publication, 22 November 2018. doi:10.11650/tjm/181109. https://projecteuclid.org/euclid.twjm/1542855636

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