On the stability of a laminated beam with structural damping and Gurt–Pipkin thermal law
Articles
Wenjun Liu
Nanjing University of Information Science and Technology
Weifan Zhao
Nanjing University of Information Science and Technology
Published 2021-05-01
https://doi.org/10.15388/namc.2021.26.23051
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Keywords

laminated beam
Gurtin–Pipkin thermal law
well-posedness
exponential stability
lack of exponential stability

How to Cite

Liu W. and Zhao W. (2021) “On the stability of a laminated beam with structural damping and Gurt–Pipkin thermal law”, Nonlinear Analysis: Modelling and Control, 26(3), pp. 396-418. doi: 10.15388/namc.2021.26.23051.

Abstract

In this paper, we investigate the stabilization of a one-dimensional thermoelastic laminated beam with structural damping coupled with a heat equation modeling an expectedly dissipative effect through heat conduction governed by Gurtin–Pipkin thermal law. Under some assumptions on the relaxation function g, we establish the well-posedness of the problem by using Lumer–Phillips theorem. Furthermore, we prove the exponential stability and lack of exponential stability depending on a stability number by using the perturbed energy method and Gearhart–Herbst–Prüss–Huang theorem, respectively.

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