Optimal energy decay rate in a damped Rayleigh beam

Bopeng Rao

doi:10.3934/dcds.1998.4.721

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1998, Volume 4, Issue 4: 721-734. Doi: 10.3934/dcds.1998.4.721

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Optimal energy decay rate in a damped Rayleigh beam

Bopeng Rao^1,

1.
Institut de Recherche Mathématique Avancée, Université Louis Pasteur de Strasbourg, 7 rue René-Descartes, 67084 Strasbourg

Received: August 1997

Revised: May 1998

Published: October 1998

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Abstract

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.

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Mathematics Subject Classification: Primary: 35C20, 35P20, 35P10, 93D15.

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