Skip to Main content Skip to Navigation
Journal articles

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

Abstract : 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 (l1,l2), 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,l1) and null on (l2,L) is reachable. Finally, when the control region is a neighborhood of the right endpoint, an exact controllability result in a weighted L2-space is also established.
Document type :
Journal articles
Complete list of metadata

https://hal-mines-paristech.archives-ouvertes.fr/hal-01261677
Contributor : François Chaplais <>
Submitted on : Monday, January 25, 2016 - 4:51:58 PM
Last modification on : Monday, October 19, 2020 - 2:34:03 PM

Links full text

Identifiers

Citation

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, EDP Sciences, 2015, 21 (4), pp.1076-1107. ⟨10.1051/cocv/2014059⟩. ⟨hal-01261677⟩

Share

Metrics

Record views

231