LOCAL CONTROLLABILITY OF THE KORTEWEG-DE VRIES EQUATION WITH THE RIGHT DIRICHLET CONTROL - Laboratoire Jacques-Louis Lions Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

LOCAL CONTROLLABILITY OF THE KORTEWEG-DE VRIES EQUATION WITH THE RIGHT DIRICHLET CONTROL

Résumé

The Korteweg-de Vries (KdV) equation with the right Dirichlet control was initially investigated by Glass and Guerrero. They showed that this system is small time locally exactly controllable for all non critical lengths and its linearized system is not controllable for all critical lengths. Even the controllability of the KdV system has been studied extensively in the last two decades, the local controllability of this system for critical lengths remains an open question. In this paper, we give a definitive answer to this question. More precisely, we show that the KdV equation with the right Dirichlet control is finite time locally exactly controllable but not small time locally null controllable for all critical lengths.
Fichier principal
Vignette du fichier
KDV-Dirichlet-Nguyen-23-02-09.pdf (517.56 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
licence

Dates et versions

hal-03982041 , version 1 (10-02-2023)
hal-03982041 , version 2 (16-05-2024)

Licence

Identifiants

  • HAL Id : hal-03982041 , version 1

Citer

Hoai-Minh Nguyen. LOCAL CONTROLLABILITY OF THE KORTEWEG-DE VRIES EQUATION WITH THE RIGHT DIRICHLET CONTROL. 2023. ⟨hal-03982041v1⟩
15 Consultations
23 Téléchargements

Partager

Gmail Mastodon Facebook X LinkedIn More