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.

Classification: 93B05, 93C20, 74K20

Keywords: Carleman estimates, exact controllability, multilayer plate, lamé system, Kirchhoff plate

@article{COCV_2011__17_4_1101_0, author = {Hansen, Scott W. and Imanuvilov, Oleg}, title = {Exact controllability of a multilayer Rao-Nakra plate with clamped boundary conditions}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, publisher = {EDP-Sciences}, volume = {17}, number = {4}, year = {2011}, pages = {1101-1132}, doi = {10.1051/cocv/2010040}, zbl = {1238.93012}, mrnumber = {2859867}, language = {en}, url = {http://www.numdam.org/item/COCV_2011__17_4_1101_0} }

Hansen, Scott W.; Imanuvilov, Oleg. Exact controllability of a multilayer Rao-Nakra plate with clamped boundary conditions. ESAIM: Control, Optimisation and Calculus of Variations, Volume 17 (2011) no. 4, pp. 1101-1132. doi : 10.1051/cocv/2010040. http://www.numdam.org/item/COCV_2011__17_4_1101_0/

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