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 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.