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Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain

Published online by Cambridge University Press:  15 August 2002

L. Rosier
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Abstract

The exact boundary controllability of linear and nonlinear Korteweg-de Vries equation on bounded domains with various boundary conditions is studied. When boundary conditions bear on spatial derivatives up to order 2, the exact controllability result by Russell-Zhang is directly proved by means of Hilbert Uniqueness Method. When only the first spatial derivative at the right endpoint is assumed to be controlled, a quite different analysis shows that exact controllability holds too. From this last result we derive the exact boundary controllability for nonlinear KdV equation on bounded domains, for sufficiently small initial and final states.

Keywords

Korteweg-de Vries equation / boundary controllability / Hilbert uniqueness method.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 2 , 1997 , pp. 33 - 55
Copyright
© EDP Sciences, SMAI, 1997

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