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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 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.

Keywords

exact controllabilitystabilizationBenjamin-Ono equationdispersive 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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