Convergent algorithm based on Carleman estimates for the recovery of a potential in the wave equation. - LAAS - Laboratoire d'Analyse et d'Architecture des Systèmes Access content directly
Journal Articles SIAM Journal on Numerical Analysis Year : 2017

Convergent algorithm based on Carleman estimates for the recovery of a potential in the wave equation.

Maya de Buhan
Sylvain Ervedoza

Abstract

This article develops the numerical and theoretical study of the 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 [BdBE13]. However, the numerical implementation of this strategy still presents several challenges, that we propose to address here.
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Dates and versions

hal-01352772 , version 1 (09-08-2016)

Identifiers

  • HAL Id : hal-01352772 , version 1

Cite

Lucie Baudouin, Maya de Buhan, Sylvain Ervedoza. Convergent algorithm based on Carleman estimates for the recovery of a potential in the wave equation.. SIAM Journal on Numerical Analysis, 2017, 55 (4), pp.1578-1613. ⟨hal-01352772⟩
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