Stabilization of coupled thermoelastic Kirchhoff plate and wave equations

We consider a coupled system consisting of a Kirchhoff thermoelastic plate and an undamped wave equation. It is known that the Kirchhoff thermoelastic plate is exponentially stable. The coupling is weak. First, we show that the coupled system is not exponentially stable. Afterwards, we prove that...

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Main Authors:	Sabeur Mansouri, Louis Tebou
Format:	Article
Language:	English
Published:	Texas State University 2020-12-01
Series:	Electronic Journal of Differential Equations
Subjects:	kirchhoff thermoelastic plate wave equation stabilization weakly coupled equations frequency domain method multipliers technique
Online Access:	http://ejde.math.txstate.edu/Volumes/2020/121/abstr.html

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spelling	doaj-b228b1563ff948118d0432cd41faae952021-03-02T15:52:27ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912020-12-012020121,116Stabilization of coupled thermoelastic Kirchhoff plate and wave equationsSabeur Mansouri0Louis Tebou1 Univ. of Monastir, Monastir, Tunisia Florida International Univ., Miami, FL, USA We consider a coupled system consisting of a Kirchhoff thermoelastic plate and an undamped wave equation. It is known that the Kirchhoff thermoelastic plate is exponentially stable. The coupling is weak. First, we show that the coupled system is not exponentially stable. Afterwards, we prove that the coupled system is polynomially stable, and provide an explicit polynomial decay rate of the associated semigroup. Our proof relies on a combination of the frequency domain method and the multipliers technique.http://ejde.math.txstate.edu/Volumes/2020/121/abstr.htmlkirchhoff thermoelastic platewave equationstabilizationweakly coupled equationsfrequency domain methodmultipliers technique
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Sabeur Mansouri Louis Tebou
spellingShingle	Sabeur Mansouri Louis Tebou Stabilization of coupled thermoelastic Kirchhoff plate and wave equations Electronic Journal of Differential Equations kirchhoff thermoelastic plate wave equation stabilization weakly coupled equations frequency domain method multipliers technique
author_facet	Sabeur Mansouri Louis Tebou
author_sort	Sabeur Mansouri
title	Stabilization of coupled thermoelastic Kirchhoff plate and wave equations
title_short	Stabilization of coupled thermoelastic Kirchhoff plate and wave equations
title_full	Stabilization of coupled thermoelastic Kirchhoff plate and wave equations
title_fullStr	Stabilization of coupled thermoelastic Kirchhoff plate and wave equations
title_full_unstemmed	Stabilization of coupled thermoelastic Kirchhoff plate and wave equations
title_sort	stabilization of coupled thermoelastic kirchhoff plate and wave equations
publisher	Texas State University
series	Electronic Journal of Differential Equations
issn	1072-6691
publishDate	2020-12-01
description	We consider a coupled system consisting of a Kirchhoff thermoelastic plate and an undamped wave equation. It is known that the Kirchhoff thermoelastic plate is exponentially stable. The coupling is weak. First, we show that the coupled system is not exponentially stable. Afterwards, we prove that the coupled system is polynomially stable, and provide an explicit polynomial decay rate of the associated semigroup. Our proof relies on a combination of the frequency domain method and the multipliers technique.
topic	kirchhoff thermoelastic plate wave equation stabilization weakly coupled equations frequency domain method multipliers technique
url	http://ejde.math.txstate.edu/Volumes/2020/121/abstr.html
work_keys_str_mv	AT sabeurmansouri stabilizationofcoupledthermoelastickirchhoffplateandwaveequations AT louistebou stabilizationofcoupledthermoelastickirchhoffplateandwaveequations
_version_	1724234569793667072

Stabilization of coupled thermoelastic Kirchhoff plate and wave equations

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