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

L. Rosier

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 2, page 33-55
  • ISSN: 1292-8119

Abstract

top
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.

How to cite

top

Rosier, L.. "Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain ." ESAIM: Control, Optimisation and Calculus of Variations 2 (2010): 33-55. <http://eudml.org/doc/116551>.

@article{Rosier2010,
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. },
author = {Rosier, L.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Korteweg-de Vries equation / boundary controllability / Hilbert uniqueness method.; controllability; Hilbert uniqueness method; boundary control; nonlinear Korteweg-de Vries equation; bounded domains; fixed point theorem},
language = {eng},
month = {3},
pages = {33-55},
publisher = {EDP Sciences},
title = {Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain },
url = {http://eudml.org/doc/116551},
volume = {2},
year = {2010},
}

TY - JOUR
AU - Rosier, L.
TI - Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 2
SP - 33
EP - 55
AB - 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.
LA - eng
KW - Korteweg-de Vries equation / boundary controllability / Hilbert uniqueness method.; controllability; Hilbert uniqueness method; boundary control; nonlinear Korteweg-de Vries equation; bounded domains; fixed point theorem
UR - http://eudml.org/doc/116551
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.