Preprint Article Version 2 This version is not peer-reviewed

Exponential and Polynomial Decay for a Laminated Beam with Fourier's Type Heat Conduction

Version 1 : Received: 16 February 2017 / Approved: 16 February 2017 / Online: 16 February 2017 (08:52:57 CET)
Version 2 : Received: 28 January 2019 / Approved: 28 January 2019 / Online: 28 January 2019 (11:14:59 CET)

How to cite: Liu, W.; Zhao, W. Exponential and Polynomial Decay for a Laminated Beam with Fourier's Type Heat Conduction. Preprints 2017, 2017020058 (doi: 10.20944/preprints201702.0058.v2). Liu, W.; Zhao, W. Exponential and Polynomial Decay for a Laminated Beam with Fourier's Type Heat Conduction. Preprints 2017, 2017020058 (doi: 10.20944/preprints201702.0058.v2).

Abstract

In this paper, we study the well-posedness and asymptotics of a one-dimensional thermoelastic laminated beam system either with or without structural damping, where the heat conduction is given by Fourier's law effective in the rotation angle displacements. We show that the system is well-posed by using Lumer-Philips theorem, and prove that the system is exponentially stable if and only if the wave speeds are equal, by using the perturbed energy method and Gearhart-Herbst-Prüss-Huang theorem. Furthermore, we show that the system with structural damping is polynomially stable provided that the wave speeds are not equal, by using the second-order energy method.

Subject Areas

laminated beam; Fourier's law; exponential stability; lack of exponential stability; polynomial stability

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