Stabilization of second order evolution equations by a class of unbounded feedbacks

Kais Ammari; Marius Tucsnak

ESAIM: Control, Optimisation and Calculus of Variations (2001)

  • Volume: 6, page 361-386
  • ISSN: 1292-8119

Abstract

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In this paper we consider second order evolution equations with unbounded feedbacks. Under a regularity assumption we show that observability properties for the undamped problem imply decay estimates for the damped problem. We consider both uniform and non uniform decay properties.

How to cite

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Ammari, Kais, and Tucsnak, Marius. "Stabilization of second order evolution equations by a class of unbounded feedbacks." ESAIM: Control, Optimisation and Calculus of Variations 6 (2001): 361-386. <http://eudml.org/doc/90598>.

@article{Ammari2001,
abstract = {In this paper we consider second order evolution equations with unbounded feedbacks. Under a regularity assumption we show that observability properties for the undamped problem imply decay estimates for the damped problem. We consider both uniform and non uniform decay properties.},
author = {Ammari, Kais, Tucsnak, Marius},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {stabilization; observability inequality; second order evolution equations; unbounded feedbacks; stabilization by feedback; infinite dimensional systems; controllability; observability; exponential stability; decay rate},
language = {eng},
pages = {361-386},
publisher = {EDP-Sciences},
title = {Stabilization of second order evolution equations by a class of unbounded feedbacks},
url = {http://eudml.org/doc/90598},
volume = {6},
year = {2001},
}

TY - JOUR
AU - Ammari, Kais
AU - Tucsnak, Marius
TI - Stabilization of second order evolution equations by a class of unbounded feedbacks
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2001
PB - EDP-Sciences
VL - 6
SP - 361
EP - 386
AB - In this paper we consider second order evolution equations with unbounded feedbacks. Under a regularity assumption we show that observability properties for the undamped problem imply decay estimates for the damped problem. We consider both uniform and non uniform decay properties.
LA - eng
KW - stabilization; observability inequality; second order evolution equations; unbounded feedbacks; stabilization by feedback; infinite dimensional systems; controllability; observability; exponential stability; decay rate
UR - http://eudml.org/doc/90598
ER -

References

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Citations in EuDML Documents

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  1. Kaïs Ammari, Mohamed Jellouli, Remark on stabilization of tree-shaped networks of strings
  2. Kaïs Ammari, Mouez Dimassi, Weyl formula with optimal remainder estimate of some elastic networks and applications
  3. Serge Nicaise, Julie Valein, Stabilization of second order evolution equations with unbounded feedback with delay
  4. Bao-Zhu Guo, Zhi-Xiong Zhang, On the well-posedness and regularity of the wave equation with variable coefficients
  5. Romain Joly, Perturbation de la dynamique des équations des ondes amorties
  6. Farah Abdallah, Serge Nicaise, Julie Valein, Ali Wehbe, Uniformly exponentially or polynomially stable approximations for second order evolution equations and some applications
  7. Ammar Moulahi, Salsabil Nouira, Stabilisation polynomiale et analytique de l’équation des ondes sur un rectangle

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