Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 121, pp. 1-16.

Title: Stabilization of coupled thermoelastic Kirchhoff plate and wave equations
       
Authors: Sabeur Mansouri (Univ. of Monastir, Monastir, Tunisia)
         Louis Tebou (Florida International Univ., Miami, FL, USA)

Abstract:
 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.