Convergent algorithm based on Carleman estimates for the recovery of a potential in the wave equation
Abstract
This article develops the numerical and theoretical study of a reconstruction algorithm of a potential in a wave equation from boundary measurements, using a cost functional built on weighted energy terms coming from a Carleman estimate. More precisely, this inverse problem for the wave equation consists in the determination of an unknown time-independent potential from a single measurement of the Neumann derivative of the solution on a part of the boundary. While its uniqueness and stability properties are already well known and studied, a constructive and globally convergent algorithm based on Carleman estimates for the wave operator was recently proposed in [L. Baudouin, M. de Buhan and S. Ervedoza, Global carleman estimates for waves and applications, Comm. Partial Differential Equations 38 (2013), no. 5]. However, the numerical implementation of this strategy still presents several challenges, that we propose to address here.
Keywords
Cite
@article{arxiv.1610.07400,
title = {Convergent algorithm based on Carleman estimates for the recovery of a potential in the wave equation},
author = {Lucie Baudouin and Maya de Buhan and Sylvain Ervedoza},
journal= {arXiv preprint arXiv:1610.07400},
year = {2016}
}