# On the controllability and stabilization of the linearized Benjamin-Ono equation

Felipe Linares; Jaime H. Ortega

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

- Volume: 11, Issue: 2, page 204-218
- ISSN: 1292-8119

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topLinares, Felipe, and Ortega, Jaime H.. "On the controllability and stabilization of the linearized Benjamin-Ono equation." ESAIM: Control, Optimisation and Calculus of Variations 11.2 (2010): 204-218. <http://eudml.org/doc/90761>.

@article{Linares2010,

abstract = {
In this work we are interested in the study of controllability and
stabilization of the linearized Benjamin-Ono equation with
periodic boundary conditions, which is a generic model for the
study of weakly nonlinear waves with nonlocal dispersion. It is
well known that the Benjamin-Ono equation has infinite number of
conserved quantities, thus we consider only controls acting in the
equation such that the volume of the solution is conserved. We
study also the stabilization with a feedback law which gives us an
exponential decay of the solutions.
},

author = {Linares, Felipe, Ortega, Jaime H.},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {exact controllability; stabilization; Benjamin-Ono
equation; dispersive equation.; Benjamin-Ono equation; dispersive equation},

language = {eng},

month = {3},

number = {2},

pages = {204-218},

publisher = {EDP Sciences},

title = {On the controllability and stabilization of the linearized Benjamin-Ono equation},

url = {http://eudml.org/doc/90761},

volume = {11},

year = {2010},

}

TY - JOUR

AU - Linares, Felipe

AU - Ortega, Jaime H.

TI - On the controllability and stabilization of the linearized Benjamin-Ono equation

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 11

IS - 2

SP - 204

EP - 218

AB -
In this work we are interested in the study of controllability and
stabilization of the linearized Benjamin-Ono equation with
periodic boundary conditions, which is a generic model for the
study of weakly nonlinear waves with nonlocal dispersion. It is
well known that the Benjamin-Ono equation has infinite number of
conserved quantities, thus we consider only controls acting in the
equation such that the volume of the solution is conserved. We
study also the stabilization with a feedback law which gives us an
exponential decay of the solutions.

LA - eng

KW - exact controllability; stabilization; Benjamin-Ono
equation; dispersive equation.; Benjamin-Ono equation; dispersive equation

UR - http://eudml.org/doc/90761

ER -

## References

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