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 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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Article dans une revue
SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2017, 55 (4), pp.1578-1613
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Dernière modification le : mardi 22 août 2017 - 01:09:51
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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, Society for Industrial and Applied Mathematics, 2017, 55 (4), pp.1578-1613. <hal-01352772>

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