Memory-Type Acoustic Boundary Stabilization of a Variable-Coefficient Wave Equation with Time-Varying Delay

Abstract. We consider the general decay of a variable-coefficient wave equation with a memory-type acoustic boundary condition and a time-varying delayed velocity term on the interior of the domain. Applying the Riemannian geometry method, convex analysis, and a suitable assumption of the time-varying delay, we obtain the energy decay rate, which is given by solutions of a first-order nonlinear, dissipative ODE under a wider assumption of the memory kernel.