Control of the surface of a fluid by a wavemaker
ESAIM: Control, Optimisation and Calculus of Variations, Volume 10 (2004) no. 3, p. 346-380

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.

DOI : https://doi.org/10.1051/cocv:2004012
Classification:  35B37,  49J20,  76B15,  93B05,  93C20
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},
     publisher = {EDP-Sciences},
     volume = {10},
     number = {3},
     year = {2004},
     pages = {346-380},
     doi = {10.1051/cocv:2004012},
     zbl = {1094.93014},
     mrnumber = {2084328},
     language = {en},
     url = {http://www.numdam.org/item/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://www.numdam.org/item/COCV_2004__10_3_346_0/

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