Global existence and general decay of solutions for a class of fourth-order viscoelastic wave equations

In this paper, an initial boundary value problem for a class of fourth-order viscoelastic wave equations is examined. Firstly, the local existence and uniqueness of solutions are proved by the linear approximation and the Faedo-Galerkin method. Next, a specified case of the original problem is considered. Then, under suitable assumptions and by continuity arguments, the corresponding problem admits a global solution. Finally, the energy estimates are reasonably constructed to show that the solution generally decays with small positive initial energy.