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

Scott W. Hansen; Oleg Yu Imanuvilov

doi:10.3934/mcrf.2011.1.189

Article Contents

2011, Volume 1, Issue 2: 189-230. Doi: 10.3934/mcrf.2011.1.189

This issue Previous Article Observability of heat processes by transmutation without geometric restrictions Next Article Strict Lyapunov functions for semilinear parabolic partial differential equations

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

Scott W. Hansen^1, and
Oleg Yu Imanuvilov^2,

1.
Department of Mathematics, Iowa State University, Ames, IA 50011
2.
Department of Mathematics, Colorado State University, Ft. Collins, CO 80523

Received: October 2010

Revised: April 2011

Published: June 2011

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Abstract

Exact controllability of a multilayer plate system with free boundary conditions are obtained by the method of Carleman estimates. The multilayer plate system is a natural multilayer generalization of a three-layer "sandwich plate'' system due to Rao and Nakra. In the multilayer version, $m$ shear deformable layers alternate with $m+1$ layers modeled under Kirchoff plate assumptions. The resulting system involves $m+1$ Lamé systems coupled with a scalar Kirchhoff plate equation. The controls are taken to be distributed in a neighborhood of the boundary. This paper is the sequel to [2] in which only clamped and hinged boundary conditions are considered.

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Mathematics Subject Classification: Primary: 93B05, 93C20; Secondary: 74K20.

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