Taiwanese Journal of Mathematics

General Decay Rates for a Laminated Beam with Memory

Zhijing Chen, Wenjun Liu, and Dongqin Chen

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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

Subjects
Primary: 34B05: Linear boundary value problems 35L05: Wave equation 93C20: Systems governed by partial differential equations 93D20: Asymptotic stability

Keywords
general stability laminated beam memory energy method

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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