Stabilization for Coupled Hyperbolic System With Memory Effects Via Minimal State Variable

In this work, we investigate the stabilization of a coupled PDE's system consisting of one Kirchhoff plate and one wave equation with memory effects. Three different cases are considered where the frictional infinite memory occurs in both equations or in one of the equations. First, we achieve the existence and uniqueness of the solution, utilizing the concept of minimal state variable. Moreover, it is shown that the coupled system is forced to polynomially decay. And by frequency domain analysis, the explicit decay rates are established, which only depend on the place of memory effect.