Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

On energy decay rate for linear damped systems

Pages: 851 - 864, Volume 8, Issue 4, October 2002      doi:10.3934/dcds.2002.8.851

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Mohammed Aassila - Institut de Recherche Mathématique Avancée, Université de Louis Pasteur de Strasbourg, 7 Rue René-Descartes, 67084 Strasbourg Cedex, France (email)

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.

Keywords:  Decay rate, asymptotic behavior, $C_0$-semigroups.
Mathematics Subject Classification:  Primary: 47D03, 35B37.

Received: April 2001;      Revised: May 2002;      Available Online: July 2002.