On energy decay rate for linear damped systems

Mohammed Aassila

doi:10.3934/dcds.2002.8.851

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2002, Volume 8, Issue 4: 851-864. Doi: 10.3934/dcds.2002.8.851

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On energy decay rate for linear damped systems

Mohammed Aassila^1,

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

Received: April 2001

Revised: May 2002

Published: October 2002

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Abstract

We study the asymptotic behavior of solutions of the damped linear system $u_{t t}(t)+Au(t)+Bu_t(t)=0, t\geq 0$ in the context of Hilbert spaces. We present abstract theorems on the decay rate, moreover an adequate example is presented to illustrate these results.

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Mathematics Subject Classification: Primary: 47D03, 35B37.

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