Internal controllability of the Korteweg-de Vries equation on a bounded domain - Archive ouverte HAL Access content directly
Journal Articles ESAIM: Control, Optimisation and Calculus of Variations Year : 2015

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.

Dates and versions

hal-01261677 , version 1 (25-01-2016)

Identifiers

Cite

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 (4), pp.1076-1107. ⟨10.1051/cocv/2014059⟩. ⟨hal-01261677⟩
93 View
0 Download

Altmetric

Share

Gmail Facebook X LinkedIn More