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

Kais Ammari; Marius Tucsnak

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

  • 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 (2010): 361-386. <http://eudml.org/doc/116574>.

@article{Ammari2010,
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},
month = {3},
pages = {361-386},
publisher = {EDP Sciences},
title = {Stabilization of second order evolution equations by a class of unbounded feedbacks},
url = {http://eudml.org/doc/116574},
volume = {6},
year = {2010},
}

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
DA - 2010/3//
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/116574
ER -

References

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