2007
DOI: 10.1016/j.jmaa.2007.01.061
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Exact boundary controllability of a shallow intrinsic shell model

Abstract: We consider a variant of a Koiter shell model based on the intrinsic geometry methods of Michael Delfour and Jean-Paul Zolésio. This model, derived in [J. Cagnol, I. Lasiecka, C. Lebiedzik, J.-P. Zolésio, Uniform stability in structural acoustic models with flexible curved walls, J. Differential Equations 186 (1) (2003) 88-121], relies heavily on the oriented distance function which describes the geometry. Here, we establish continuous observability estimates in the Dirichlet case with an explicit observabilit… Show more

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Cited by 5 publications
(3 citation statements)
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“…measure how well the initial conditions (y 0 , y 1 ) are recovered by the algorithm (recall that they are obtained from the system (15)). The H −1 norm of any scalar function v is computed writting that v H −1 (ω) = |w| H 1 (ω) with |w| H 1 (ω) = ( ω |∇w| 2 dξ) 1/2 and w ∈ H 1 0 (ω) is the solution of the Dirichlet problem : −∆w = v in ω, w = 0 on ∂ω.…”
Section: Analysis With Respect To Hmentioning
confidence: 99%
See 1 more Smart Citation
“…measure how well the initial conditions (y 0 , y 1 ) are recovered by the algorithm (recall that they are obtained from the system (15)). The H −1 norm of any scalar function v is computed writting that v H −1 (ω) = |w| H 1 (ω) with |w| H 1 (ω) = ( ω |∇w| 2 dξ) 1/2 and w ∈ H 1 0 (ω) is the solution of the Dirichlet problem : −∆w = v in ω, w = 0 on ∂ω.…”
Section: Analysis With Respect To Hmentioning
confidence: 99%
“…According to this property, relaxed exact spectral [24] or partial [16] controllability of membrane shells have been studied. For ε > 0, we also mention [20] where a controllability result is obtained for a shallow Koiter's shell using the Hilbert Uniqueness Method [18] and more recently [15] in the context of so-called intrinsic shell model. Furthermore, on the related thematic of stabilization, let us mention [4,14] where dissipative terms are added on the shell model in order to obtain a specific decay of the corresponding energy.…”
Section: Introductionmentioning
confidence: 99%
“…Other attempts to parametrization-free formulations of the Kirchhoff-Love shell theory are found, e.g., in [11,12,13,14] with a mathematical focus and in [33,47,50] from an engineering perspective, however, only with focus on displacements. Herein, the Kirchhoff-Love shell theory is recasted in the frame of the TDC including all relevant mechanical aspects.…”
Section: Introductionmentioning
confidence: 99%