Wave Equation with a Nonlinear Internal Dissipation

In this chapter we study the decay rate of the solutions of the wave equation in the presence of nonlinear damping terms distributed and acting everywhere in the interior of the domain. We introduce and use LaSalle's invariance principle and build suitable Lyapunov functionals, as perturbations of the energy, allowing to get explicit decay rates as a function of the dissipative nonlinearity.