Internal stabilization of a Mindlin-Timoshenko model by interior feedbacks

Serge Nicaise

doi:10.3934/mcrf.2011.1.331

Article Contents

2011, Volume 1, Issue 3: 331-352. Doi: 10.3934/mcrf.2011.1.331

This issue Previous Article Global Carleman estimate on a network for the wave equation and application to an inverse problem Next Article Global stabilization of a coupled system of two generalized Korteweg-de Vries type equations posed on a finite domain

Internal stabilization of a Mindlin-Timoshenko model by interior feedbacks

Serge Nicaise^1,

1.
Université de Valenciennes et du Hainaut Cambrésis, LAMAV, FR CNRS 2956, Institut des Sciences et Techniques of Valenciennes, F-59313 - Valenciennes Cedex 9

Received: February 2011

Revised: June 2011

Published: September 2011

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Abstract

A Mindlin-Timoshenko model with non constant and non smooth coefficients set in a bounded domain of $\mathbb{R}^d, d\geq 1$ with some internal dissipations is proposed. It corresponds to the coupling between the wave equation and the dynamical elastic system. If the dissipation acts on both equations, we show an exponential decay rate. On the contrary if the dissipation is only active on the elasticity equation, a polynomial decay is shown; a similar result is proved in one dimension if the dissipation is only active on the wave equation.

Keywords:

Mindlin-Timoshenko system,
stabilization.

Mathematics Subject Classification: Primary: 35Q74, 93D15; Secondary: 35L10.

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