Energy decay estimates for a two-dimensional coupled wave-plate system with localized frictional damping

This paper is devoted to the energy decay estimates for the two-dimensional coupled wave-plate system with local frictional damping in a bounded domain. The frictional damping is only distributed in the part of the plate's or wave's domain, and the other is stabilized by the transmission through the interface of the plate's and wave's domains. Using the frequency domain approach and the multiplier technique, we show respectively that the energy of the system decays polynomially under some geometric condition when the frictional damping only acts on the part of the plate, and the energy of the system is exponentially stable when the frictional damping acts only on the other part of the wave.