Lipschitz stability in an inverse problem for the Korteweg-de Vries equation on a finite domain

Abstract

Abstract In this paper, we address an inverse problem for the Korteweg-de Vries equation posed on a bounded domain with boundary conditions proposed by Colin and Ghidaglia. More precisely, we retrieve the principal coefficient from the measurements of the solution on a part of the boundary and also at some positive time in the whole space domain. The Lipschitz stability of this inverse problem relies on a Carleman estimate for the linearized Korteweg-de Vries equation and the Bukhgeı̌m-Klibanov method.

Keywords

• inverse problem
• Korteweg-de Vries equation
• Carleman estimate