Electron. J. Differential Equations, Vol. 2020 (2020), No. 121, pp. 1-16.

Stabilization of coupled thermoelastic Kirchhoff plate and wave equations

Sabeur Mansouri, Louis Tebou

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.

Submitted January 28, 2020. Published December 16, 2020.
Math Subject Classifications: 93D20, 35L05, 47D06, 47N70, 74F05, 74K20.
Key Words: Kirchhoff thermoelastic plate; wave equation; stabilization; weakly coupled equations; frequency domain method; multipliers technique.

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Sabeur Mansouri
Department of Mathematics
Faculty of Sciences of Monastir
University of Monastir
5019 Monastir, Tunisia
email: m.sabeur1@gmail.com
Louis Tebou
Department of Mathematics and Statistics
Florida International University
Miami, FL 33199, USA
email: teboul@fiu.edu

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