The control of the surface of water in a long canal by means of a wavemaker is investigated. The fluid motion is governed by the Korteweg-de Vries equation in lagrangian coordinates. The null controllability of the elevation of the fluid surface is obtained thanks to a Carleman estimate and some weighted inequalities. The global uncontrollability is also established.
Keywords: Korteweg-de Vries equation, lagrangian coordinates, exact boundary controllability, Carleman estimate
@article{COCV_2004__10_3_346_0, author = {Rosier, Lionel}, title = {Control of the surface of a fluid by a wavemaker}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {346--380}, publisher = {EDP-Sciences}, volume = {10}, number = {3}, year = {2004}, doi = {10.1051/cocv:2004012}, mrnumber = {2084328}, zbl = {1094.93014}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv:2004012/} }
TY - JOUR AU - Rosier, Lionel TI - Control of the surface of a fluid by a wavemaker JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2004 SP - 346 EP - 380 VL - 10 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv:2004012/ DO - 10.1051/cocv:2004012 LA - en ID - COCV_2004__10_3_346_0 ER -
%0 Journal Article %A Rosier, Lionel %T Control of the surface of a fluid by a wavemaker %J ESAIM: Control, Optimisation and Calculus of Variations %D 2004 %P 346-380 %V 10 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv:2004012/ %R 10.1051/cocv:2004012 %G en %F COCV_2004__10_3_346_0
Rosier, Lionel. Control of the surface of a fluid by a wavemaker. ESAIM: Control, Optimisation and Calculus of Variations, Volume 10 (2004) no. 3, pp. 346-380. doi : 10.1051/cocv:2004012. http://archive.numdam.org/articles/10.1051/cocv:2004012/
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