Exponential stability of a variable coefficient semilinear wave equation with viscoelastic acoustic boundary conditions

In this paper, we consider a variable coefficient semilinear wave equation with viscoelastic nonlocally acoustic boundary conditions. Such boundary conditions can describe the viscoelastic properties of elastic materials at the boundary, and can more accurately describe the propagation and reflection characteristics of sound waves at the material boundary. By the potential well method, we get the global existence of solution. Furthermore together with the energy method and the multiply method, we obtain the exponential decay result of energy. The obtained results of this paper generalize and improve some earlier results.