In this thesis, the main aim is to study the global existence and the stabilization of solutions for linear damped and viscoelastic wave equations evolving on a bounded medium in an arbitrarily large time interval subject to inhomogeneous Neumann manipulation on a part of the boundary. The analysis of these models reveals additional interesting features and challenges in comparison to their homogeneous counterparts, on which there are studies in the literature. This is due to the fact that, in the present context, the rate at which energy of solution is changed has a dependency on the boundary trace of temporal derivative. It is not clear how this quantity could be controlled in terms of given data according to Sobolev trace theory. Nevertheless, we achieve to establish global existence of solutions first using dynamic extension method to homogenize boundary conditions. Next, we construct the weak solutions of the homogenized models. For the damped wave equation, we rely on the semigroup approach while for the viscoelastic model we use Faedo-Galerkin method. The global unique solutions of the original models are obtained through a reunification argument. Then, we also prove uniform stabilization of solutions with decay rates characterized by the decay behavior of Neumann input using the multiplier (energy) technique. The latter requires a subtle analysis of boundary integrals in energy estimates involving unknown trace terms. We also develop numerical solutions of the models. For the damped wave equation, we rely on the explicit method while for the viscoelastic model we use the Crank-Nicolson method. We support our theoretical result with numerical simulations satisfying given assumptions. We supplement these with further numerical simulations in which data do not necessarily satisfy the given assumptions for decay. The latter offers, at the numerical level, essential physical insights into how energy might change in the presence of, for instance, improper boundary data