This paper is concerned with the control properties of the Korteweg–de Vries (KdV) equation posed on a bounded interval with a distributed control. When the control region is an arbitrary open subdomain , we prove the null controllability of the KdV equation by means of a new Carleman inequality. As a consequence, we obtain a regional controllability result, which roughly tells us that any target function arbitrarily chosen on and null on is reachable. Finally, when the control region is a neighborhood of the right endpoint, an exact controllability result in a weighted -space is also established.
DOI: 10.1051/cocv/2014059
Keywords: KdV equation, Carleman estimate, null controllability, exact controllability
@article{COCV_2015__21_4_1076_0, author = {Capistrano{\textendash}Filho, Roberto A. and Pazoto, Ademir F. and Rosier, Lionel}, title = {Internal controllability of the korteweg{\textendash}de vries equation on a bounded domain}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {1076--1107}, publisher = {EDP-Sciences}, volume = {21}, number = {4}, year = {2015}, doi = {10.1051/cocv/2014059}, mrnumber = {3395756}, zbl = {1331.35302}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv/2014059/} }
TY - JOUR AU - Capistrano–Filho, Roberto A. AU - Pazoto, Ademir F. AU - Rosier, Lionel TI - Internal controllability of the korteweg–de vries equation on a bounded domain JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2015 SP - 1076 EP - 1107 VL - 21 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2014059/ DO - 10.1051/cocv/2014059 LA - en ID - COCV_2015__21_4_1076_0 ER -
%0 Journal Article %A Capistrano–Filho, Roberto A. %A Pazoto, Ademir F. %A Rosier, Lionel %T Internal controllability of the korteweg–de vries equation on a bounded domain %J ESAIM: Control, Optimisation and Calculus of Variations %D 2015 %P 1076-1107 %V 21 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2014059/ %R 10.1051/cocv/2014059 %G en %F COCV_2015__21_4_1076_0
Capistrano–Filho, Roberto A.; Pazoto, Ademir F.; Rosier, Lionel. Internal controllability of the korteweg–de vries equation on a bounded domain. ESAIM: Control, Optimisation and Calculus of Variations, Volume 21 (2015) no. 4, pp. 1076-1107. doi : 10.1051/cocv/2014059. http://www.numdam.org/articles/10.1051/cocv/2014059/
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