Stabilisation frontière de problèmes de Ventcel

Amar Heminna

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 5, page 591-622
  • ISSN: 1292-8119

Abstract

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The problem of boundary stabilization for the isotropic linear elastodynamic system and the wave equation with Ventcel's conditions are considered (see [12]). The boundary observability and the exact controllability were etablished in [11]. We prove here the enegy decay to zero for the elastodynamic system with stationary Ventcel's conditions by introducing a nonlinear boundary feedback. We also give a boundary feedback leading to arbitrarily large energy decay rates for the elastodynamic system with evolutive Ventcel's conditions. A spectral study proves, finally, that the natural feedback is not sufficient to assure the exponential decay in the case of the wave equation with Ventcel's conditions.

How to cite

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Heminna, Amar. "Stabilisation frontière de problèmes de Ventcel." ESAIM: Control, Optimisation and Calculus of Variations 5 (2010): 591-622. <http://eudml.org/doc/197334>.

@article{Heminna2010,
abstract = { The problem of boundary stabilization for the isotropic linear elastodynamic system and the wave equation with Ventcel's conditions are considered (see [12]). The boundary observability and the exact controllability were etablished in [11]. We prove here the enegy decay to zero for the elastodynamic system with stationary Ventcel's conditions by introducing a nonlinear boundary feedback. We also give a boundary feedback leading to arbitrarily large energy decay rates for the elastodynamic system with evolutive Ventcel's conditions. A spectral study proves, finally, that the natural feedback is not sufficient to assure the exponential decay in the case of the wave equation with Ventcel's conditions. },
author = {Heminna, Amar},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Élasticité; ondes; problème de Ventcel; contrôlabilité; stabilisation.; elastodynamic systems; wave equation; Venttsel problem; nonlinear boundary feedback; boundary stabilization; energy decay rates; exponential decay},
language = {fre},
month = {3},
pages = {591-622},
publisher = {EDP Sciences},
title = {Stabilisation frontière de problèmes de Ventcel},
url = {http://eudml.org/doc/197334},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Heminna, Amar
TI - Stabilisation frontière de problèmes de Ventcel
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 5
SP - 591
EP - 622
AB - The problem of boundary stabilization for the isotropic linear elastodynamic system and the wave equation with Ventcel's conditions are considered (see [12]). The boundary observability and the exact controllability were etablished in [11]. We prove here the enegy decay to zero for the elastodynamic system with stationary Ventcel's conditions by introducing a nonlinear boundary feedback. We also give a boundary feedback leading to arbitrarily large energy decay rates for the elastodynamic system with evolutive Ventcel's conditions. A spectral study proves, finally, that the natural feedback is not sufficient to assure the exponential decay in the case of the wave equation with Ventcel's conditions.
LA - fre
KW - Élasticité; ondes; problème de Ventcel; contrôlabilité; stabilisation.; elastodynamic systems; wave equation; Venttsel problem; nonlinear boundary feedback; boundary stabilization; energy decay rates; exponential decay
UR - http://eudml.org/doc/197334
ER -

References

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