General decay rate of a variable coefficient wave equation with boundary viscoelastic damping

Abstract In this paper, we consider the general decay of wave equation with variable coefficients and boundary viscoelastic damping. Applying the Riemannian geometry method and convex analysis, we establish the energy decay rate which is given by solutions of a first‐order nonlinear, dissipative ordinary differential equation under a wider assumption of the viscoelastic damping and some conditions on the coefficient matrix.