Boundary Stabilization of the Wave Equation

In this chapter we study the boundary stabilization of the wave equation. We apply LaSalle’s Invariance Principle and show the decay of finite energy solutions under general conditions on the partition of the boundary and on the nonlinearity. We also prove explicit decay rates under suitable assumptions on the damping term. In addition, we present a second proof of the exponential decay for the linear dissipation, of interest when dealing with model perturbations.