Exact controllability of a multilayer Rao-Nakra plate with clamped boundary conditions

Scott W. Hansen; Oleg Imanuvilov

ESAIM: Control, Optimisation and Calculus of Variations (2011)

  • Volume: 17, Issue: 4, page 1101-1132
  • ISSN: 1292-8119

Abstract

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Exact controllability results 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 “sandwich plate” system due to Rao and Nakra. The multilayer version involves a number of Lamé systems for plane elasticity coupled with a scalar Kirchhoff plate equation. The plate is assumed to be either clamped or hinged and controls are assumed to be locally distributed in a neighborhood of a portion of the boundary. The Carleman estimates developed for the coupled 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.

How to cite

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Hansen, Scott W., and Imanuvilov, Oleg. "Exact controllability of a multilayer Rao-Nakra plate with clamped boundary conditions." ESAIM: Control, Optimisation and Calculus of Variations 17.4 (2011): 1101-1132. <http://eudml.org/doc/276325>.

@article{Hansen2011,
abstract = { Exact controllability results 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 “sandwich plate” system due to Rao and Nakra. The multilayer version involves a number of Lamé systems for plane elasticity coupled with a scalar Kirchhoff plate equation. The plate is assumed to be either clamped or hinged and controls are assumed to be locally distributed in a neighborhood of a portion of the boundary. The Carleman estimates developed for the coupled 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. },
author = {Hansen, Scott W., Imanuvilov, Oleg},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Carleman estimates; exact controllability; multilayer plate; Lamé system; Kirchhoff plate; exact controllability results; multilayer plate system; method of Carleman estimates},
language = {eng},
month = {11},
number = {4},
pages = {1101-1132},
publisher = {EDP Sciences},
title = {Exact controllability of a multilayer Rao-Nakra plate with clamped boundary conditions},
url = {http://eudml.org/doc/276325},
volume = {17},
year = {2011},
}

TY - JOUR
AU - Hansen, Scott W.
AU - Imanuvilov, Oleg
TI - Exact controllability of a multilayer Rao-Nakra plate with clamped boundary conditions
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2011/11//
PB - EDP Sciences
VL - 17
IS - 4
SP - 1101
EP - 1132
AB - Exact controllability results 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 “sandwich plate” system due to Rao and Nakra. The multilayer version involves a number of Lamé systems for plane elasticity coupled with a scalar Kirchhoff plate equation. The plate is assumed to be either clamped or hinged and controls are assumed to be locally distributed in a neighborhood of a portion of the boundary. The Carleman estimates developed for the coupled 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.
LA - eng
KW - Carleman estimates; exact controllability; multilayer plate; Lamé system; Kirchhoff plate; exact controllability results; multilayer plate system; method of Carleman estimates
UR - http://eudml.org/doc/276325
ER -

References

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