Rapid exponential stabilization for a linear Korteweg-de Vries equation

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May 2009, 11(3): 655-668. doi: 10.3934/dcdsb.2009.11.655

Rapid exponential stabilization for a linear Korteweg-de Vries equation

Eduardo Cerpa ^1, and Emmanuelle Crépeau ^2,

1.	Laboratoire de Mathématiques, Université Paris-Sud 11, Bât. 425, 91405 Orsay Cedex, France
2.	INRIA Rocquencourt, Domaine de Voluceau, 78150 Le Chesnay, France

Received February 2008 Revised November 2008 Published March 2009

Abstract
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We consider a control system for a Korteweg-de Vries equation with homogeneous Dirichlet boundary conditions and Neumann boundary control. We address the rapid exponential stabilization problem. More precisely, we build some feedback laws forcing the solutions of the closed-loop system to decay exponentially to zero with arbitrarily prescribed decay rates. We also perform some numerical computations in order to illustrate this theoretical result.

Keywords: controllability, feedback., stabilization, Korteweg-de Vries equation.

Mathematics Subject Classification: Primary: 93D15, 35Q53; Secondary: 93B0.

Citation: Eduardo Cerpa, Emmanuelle Crépeau. Rapid exponential stabilization for a linear Korteweg-de Vries equation. Discrete & Continuous Dynamical Systems - B, 2009, 11 (3) : 655-668. doi: 10.3934/dcdsb.2009.11.655

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