Stability for variable-coefficient wave equation with local frictional damping and memory type dynamic boundary conditions

We investigate a variable-coefficient wave equation with interior local frictional damping and memory-type dynamic boundary conditions. The innovation of the paper lies in the presence of dynamic boundary conditions, thus we need some special techniques to deal with the high-order terms on the boundary. By the Riemannian geometry method and the multiplier technique, we establish the stable results, and the energy decay result of system is described by employing the solution of a stable first-order ordinary differential equation. The stability depends on the frictional damping function and kernel function, thereby improving and generalizing the results of prior references.