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

Boundary value problems

Mo Chen¹ 

[1] School of Mathematics and Statistics, Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun, P.R. China

关键词: inverse problem;    Korteweg-de Vries equation;    Carleman estimate;    35R30;    35Q53;   

DOI  :  10.1186/s13661-017-0779-8

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY