Stabilization for Transmission Wave-Plate Equations with Acoustic/Memory Boundary Conditions

In this paper, we consider a transmission system of wave equation and Euler–Bernoulli equation with boundary memory effects and acoustic boundary conditions. By using two inverse Volterra’s operators we take some transformations such that the memory terms do not appear explicitly on the boundary, and we get an equivalent system. Combining Faedo–Galerkin’s method and compactness arguments, we prove the local existence and uniqueness of weak solution. With different assumptions on the relaxation functions, we establish several explicit decay results relying on Riemannian multiplier method, which has improved the previous results in the literature.