Internal controllability of the Korteweg-de Vries equation on a bounded domain
Analysis of PDEs
2021-05-03 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1401.6833,
title = {Internal controllability of the Korteweg-de Vries equation on a bounded domain},
author = {Roberto Capistrano Filho and Ademir Pazoto and Lionel Rosier},
journal= {arXiv preprint arXiv:1401.6833},
year = {2021}
}