Stability of an inverse problem for the discrete wave equation and convergence results
Author
dc.contributor.author
Baudouin, Lucie
Author
dc.contributor.author
Ervedoza, Sylvain
Author
dc.contributor.author
Osses Alvarado, Axel
Admission date
dc.date.accessioned
2015-08-04T18:09:45Z
Available date
dc.date.available
2015-08-04T18:09:45Z
Publication date
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2015
Cita de ítem
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J. Math. Pures Appl. 103 (2015) 1475–1522
en_US
Identifier
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0021-7824
Identifier
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10.1016/j.matpur.2014.11.006
Identifier
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https://repositorio.uchile.cl/handle/2250/132340
Abstract
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Using uniform global Carleman estimates for semi-discrete elliptic and hyperbolic equations, we study Lipschitz and logarithmic stability for the inverse problem of recovering a potential in a semi-discrete wave equation, discretized by finite differ-ences in a 2-d uniform mesh, from boundary or internal measurements. The discrete stability results, when compared with their continuous counterparts, include new terms depending on the discretization parameter h. From these stability results, we design a numerical method to compute convergent approximations of the continuous potential.
en_US
Patrocinador
dc.description.sponsorship
Math-AmSud project COSIP “Control Systems and Identification Problems”, Fondecyt-1110290, Conicyt-ACT1106 grants
and University Paul Sabatier (Toulouse 3), AO PICAN