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

Abstract

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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.

How to cite

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Linares, 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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