Stability of the vibrations of a damped general inhomogeneous wave equation

Abstract

In this paper, we consider the vibrations of an inhomogeneous damped wave under distributed disturbing force. The well-possedness of the system is studied. We prove that the amplitude of such vibrations is bounded under some restriction of the disturbing force. Finally, we establish the uniform exponential stabilization of the system when the disturbing force is insignicant. The results are established directly by means of an exponential energy decay estimate.