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J. Lagnese, “Decay of Solutions of Wave Equations in a Bounded Region with Boundary Dissipation,” Journal of Differential Equations, Vol. 50, No. 2, 1983, pp. 163-182. doi:10.1016/0022-0396(83)90073-6

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.