Neumann-boundary stabilization of the wave equation with damping control and applications

This article is devoted to the boundary stabilization of a non-homogeneous ndimensional wave equation subject to static or dynamic Neumann boundary conditions. Using a linear feedback law involving only a damping term, we provide a simple method and obtain an asymptotic convergence result for the solutions of the considered systems. The method consists in proposing a new energy norm. Then, a similar result is derived for the case of dynamic Neumann boundary conditions with nonlinear damping feedback laws. Finally, the method presented in this work is also applied to several distributed parameter systems such as the Petrovsky system, coupled wave-wave equations and elasticity systems.