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On the controllability and stabilization ofthe linearized Benjamin-Ono equation

Published online by Cambridge University Press:  15 March 2005

Felipe Linares  and
Jaime H. Ortega
Felipe Linares
Affiliation:
IMPA, Estrada Dona Castorina 110, Rio de Janeiro, 22460-320, Brasil; linares@impa.br
Jaime H. Ortega
Affiliation:
Universidad de Chile, Facultad de Ciencias Físicas y Matemáticas. Departamento de Ingeniería Matemática, Casilla 170/3, Correo 3, Santiago, Chile. Departamento de Ciencias Básicas, Universidad del Bío-Bío, Avda. Andrés Bello s/n, Casilla 447, Chillán, Chile; jortega@dim.uchile.cl
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Abstract

In this work we are interested in the study of controllability andstabilization of the linearized Benjamin-Ono equation withperiodic boundary conditions, which is a generic model forthestudy of weakly nonlinear waves with nonlocal dispersion. It iswell known that theBenjamin-Ono equation has infinite number ofconserved quantities, thus we consider only controls acting in theequation such that the volume of the solution is conserved. Westudy also the stabilization with a feedback law which gives us anexponential decay of the solutions.

Keywords

exact controllabilitystabilizationBenjamin-Onoequationdispersive equation.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 11 , Issue 2 , April 2005 , pp. 204 - 218
Copyright
© EDP Sciences, SMAI, 2005

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