Neumann-Boundary Stabilization of the Wave Equation with Internal Damping Control and Applications

Abstract

This paper is devoted to the Neumann boundary stabilization of a non-homogeneous ndimensional wave equation subject to static or dynamic boundary conditions. Using a linear feedback law involving only an internal term, we prove the well-posedness of the considered systems and provide a simple method to obtain an asymptotic convergence result for the solutions. The method consists of proposing a new energy norm, and applying the semigroup theory and LaSalle's principle. 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 elastic system.