Internal controllability of the Korteweg-de Vries equation on a bounded domain

Roberto Capistrano Filho (1) , Ademir Pazoto (1) , Lionel Rosier (2)

1 IM / UFRJ - Instituto de Matemática da Universidade Federal do Rio de Janeiro
2 CAS - Centre Automatique et Systèmes

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, the state function being controlled on the left part of the complement of the control region. Finally, when the control region is a neighborhood of the right endpoint, an exact controllability result in a weighted L2 space is also established.

Mots clés: KdV equation; Carleman estimate; null controllability; exact controllability

Domaines: Equations aux dérivées partielles [math.AP]

Roberto Capistrano Filho, Ademir Pazoto, Lionel Rosier. Internal controllability of the Korteweg-de Vries equation on a bounded domain. ESAIM: Control, Optimisation and Calculus of Variations, 2015, 21, pp.1076-1107. ⟨hal-00936728⟩