Geodesic
Internal controllability of the korteweg–de vries equation on a bounded domain
Capistrano–Filho, Roberto A.1, 2  ; Pazoto, Ademir F.3  ; Rosier, Lionel4 
1 Instituto de Matemática, Universidade Federal do Rio de Janeiro, C.P. 68530, Cidade Universitária, Ilha do Fundão, 21941-909 Rio de Janeiro (RJ), Brazil.
2 Institut Elie Cartan, UMR 7502 UHP/CNRS/INRIA, BP 70239, 54506 Vandœuvre-les-Nancy cedex, France.
3 Instituto de Matemática, Universidade Federal do Rio de Janeiro, C.P. 68530, Cidade Universitária, Ilha do Fundão, 21941-909 Rio de Janeiro (RJ), Brazil.
4 Centre Automatique et Systèmes, MINES ParisTech, PSL Research University, 60 boulevard Saint-Michel, 75272 Paris cedex 06, France.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 4, pp. 1076-1107 Cet article a éte moissonné depuis la source Numdam

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This paper is concerned with the control properties of the Korteweg–de Vries (KdV) equation posed on a bounded interval (0,L) with a distributed control. When the control region is an arbitrary open subdomain (l 1 ,l 2 ), 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 (0,l 1 ) and null on (l 2 ,L) is reachable. Finally, when the control region is a neighborhood of the right endpoint, an exact controllability result in a weighted L 2 -space is also established.

DOI : 10.1051/cocv/2014059
Classification : 35Q53, 37K10, 93B05, 93D15
Keywords: KdV equation, Carleman estimate, null controllability, exact controllability

Capistrano–Filho, Roberto A. 1, 2 ; Pazoto, Ademir F. 3 ; Rosier, Lionel 4

1 Instituto de Matemática, Universidade Federal do Rio de Janeiro, C.P. 68530, Cidade Universitária, Ilha do Fundão, 21941-909 Rio de Janeiro (RJ), Brazil.
2 Institut Elie Cartan, UMR 7502 UHP/CNRS/INRIA, BP 70239, 54506 Vandœuvre-les-Nancy cedex, France.
3 Instituto de Matemática, Universidade Federal do Rio de Janeiro, C.P. 68530, Cidade Universitária, Ilha do Fundão, 21941-909 Rio de Janeiro (RJ), Brazil.
4 Centre Automatique et Systèmes, MINES ParisTech, PSL Research University, 60 boulevard Saint-Michel, 75272 Paris cedex 06, France. 
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     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},
     year = {2015},
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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, Tome 21 (2015) no. 4, pp. 1076-1107. doi: 10.1051/cocv/2014059

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