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Exact controllability of a multilayer Rao-Nakra platewith clamped boundary conditions

Published online by Cambridge University Press:  08 November 2010

Scott W. Hansen  and
Oleg Imanuvilov
Scott W. Hansen
Affiliation:
Department of Mathematics, Iowa State University, Ames, IA 50011, [email protected] .
Oleg Imanuvilov
Affiliation:
Department of Mathematics, Colorado State University, Ft. Collins, CO 80523, USA.
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Abstract

Exact controllabilityresults for a multilayer plate system are obtained from the method of Carleman estimates.The multilayer plate system is a natural multilayer generalization of a classical three-layer “sandwichplate” system due to Rao and Nakra. The multilayer version involves a number ofLamé systems for plane elasticity coupled with a scalar Kirchhoff plate equation. The plate is assumed to be either clamped or hinged and controlsare assumed to be locally distributed in a neighborhood of a portion of the boundary. The Carleman estimates developed for thecoupled system are based on some new Carleman estimates for the Kirchhoff plate as well as some known Carleman estimates due to Imanuvilov and Yamamoto for the Lamé system.

Keywords

Carleman estimatesexact controllabilitymultilayer plateLamé systemKirchhoff plate
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 17 , Issue 4 , October 2011 , pp. 1101 - 1132
Copyright
© EDP Sciences, SMAI, 2010

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