Indirect stability of a 2D wave-plate coupling system with memory viscoelastic damping

We performed a stability analysis of a 2D wave-plate coupling system equipped with memory viscoelastic damping. The study highlights the unique functionality of the damping mechanism, which operates indirectly and exclusively within either the wave or plate subsystem. The opposing subsystem receives dissipative signals indirectly through the coupling component. The primary objective of this study was to determine whether the indirect memory damping is sufficient to ensure the overall stability of the coupled system. To address this question, a frequency domain analysis was employed to establish explicit decay rates of the coupled system. Notably, a polynomial decay rate is observed when the memory damping is applied solely to either the plate or wave subsystem, which provides a conclusive answer to the posed question.