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October  1998, 4(4): 721-734. doi: 10.3934/dcds.1998.4.721

Optimal energy decay rate in a damped Rayleigh beam

1. 

Institut de Recherche Mathématique Avancée, Université Louis Pasteur de Strasbourg, 7 rue René-Descartes, 67084 Strasbourg, France

Received  August 1997 Revised  May 1998 Published  July 1998

We consider a clamped Rayleigh beam subject to a positive viscous damping. Using an explicit approximation, we first give the asymptotic expansion of eigenvalues and eigenfunctions of the underlying system. We next identify the optimal energy decay rate of the system with the supremum of the real part of the spectrum of the infinitesimal generator of the associated semigroup.
Citation: Bopeng Rao. Optimal energy decay rate in a damped Rayleigh beam. Discrete and Continuous Dynamical Systems, 1998, 4 (4) : 721-734. doi: 10.3934/dcds.1998.4.721
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