On the determination of the principal coefficient from boundary measurements in a KdV equation

Lucie Baudouin (1) , Eduardo Cerpa (2) , Emmanuelle Crépeau (3) , Alberto Mercado (4)

1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
2 Departamento de Matematica [Valparaiso]
3 LMV - Laboratoire de Mathématiques de Versailles
4 CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago]

This paper concerns the inverse problem of retrieving the principal coefficient in a Korteweg-de Vries (KdV) equation from boundary measurements of a single solution. The Lipschitz stability of this inverse problem is obtained using a new global Carleman estimate for the linearized KdV equation. The proof is based on the Bukhge˘ım-Klibanov method.

Mots clés: Inverse problem; Korteweg-de Vries equation; Carleman estimate

Domaines: Equations aux dérivées partielles [math.AP]

Lucie Baudouin, Eduardo Cerpa, Emmanuelle Crépeau, Alberto Mercado. On the determination of the principal coefficient from boundary measurements in a KdV equation. 2012. ⟨hal-00765919v1⟩