J. L. Lions, “Exact Controllability, Stabilization and Perturbations for Distributed Systems,” SIAM Review, Vol. 30, No. 1, 1988, pp. 1-68. doi:10.1137/1030001
has been cited by the following article:
TITLE: A Note on Stability of Longitudinal Vibrations of an Inhomogeneous Beam
AUTHORS: Prasanta Kumar Nandi, Ganesh Chandra Gorain, Samarjit Kar
KEYWORDS: Inhomogeneous Beam; Longitudinal Vibrations; Uniform Stabilization; Energy Decay Estimate
JOURNAL NAME: Applied Mathematics, Vol.3 No.1, January 4, 2012
ABSTRACT: In this paper, we have considered an inhomogeneous beam with a damping distributed along the length of the beam. The beam is clamped at both ends and is assumed to vibrate longitudinally. We have estimated the total energy of the system at any time t. By constructing suitable Lyapunov functional, it is established directly that the energy of this system decays exponentially.