Stability of Wave Equation with Variable Coefficients by Boundary Fractional Dissipation Law

In this paper, we consider the boundary stability of the wave equation with variable coefficients and fractional damping acting on part of the boundary. The acceleration terms on the boundary are involved as well. It has been known that the presence of such dynamic structures on the boundary may change drastically the stability property of the underlying system. We obtain the polynomial decay for the solutions by applying a boundary fractional dissipation law. Our proof relies on the geometric multiplier skill and frequency domain method.