On the controllability and stabilization of the linearized Benjamin-Ono equation
ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 2, pp. 204-218.

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.

DOI : 10.1051/cocv:2005002
Classification : 37L50, 93B05, 93C20, 93D15
Mots-clés : exact controllability, stabilization, Benjamin-Ono equation, dispersive equation 
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     title = {On the controllability and stabilization of the linearized {Benjamin-Ono} equation},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {204--218},
     publisher = {EDP-Sciences},
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Linares, Felipe; Ortega, Jaime H. On the controllability and stabilization of the linearized Benjamin-Ono equation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 2, pp. 204-218. doi : 10.1051/cocv:2005002. http://www.numdam.org/articles/10.1051/cocv:2005002/

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