Stabilization of coupled thermoelastic Kirchhoff plate and wave equations

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.
 For more information see https://ejde.math.txstate.edu/Volumes/2020/121/abstr.html

Stabilization for weakly coupled string–riser system with partial frictional damping

“…There are also some papers on the control of the stability of coupled systems by the dissipation mechanism of heat. We can refer to previous studies [15][16][17][18] and the corresponding references. Other papers on the coupled systems with memory viscoelastic terms and Kelvin-Voigt damping have also been studied, which can be referred to previous studies [19][20][21][22][23] and the related references.…”