[Estimation de stabilité lipschitzienne de coefficients de Robin pour le système de Stokes]
Nous nous intéressons à lʼidentification dʼun coefficient de Robin défini sur une partie non accessible du bord, à partir de mesures disponibles sur une autre partie de celui-ci, dans le système de Stokes non stationnaire. Nous prouvons une estimation de stabilité lipschitzienne sous lʼhypothèse a priori que le coefficient de Robin est défini dans un sous-ensemble compact et convexe dʼun sous-espace vectoriel de dimension finie de lʼespace des fonctions continues. Pour ce faire, nous utilisons un théorème prouvé par L. Bourgeois permettant dʼétablir des inégalités de stabilité lipschitzienne pour une classe de problèmes inverses dans un cadre abstrait.
We are interested in the inverse problem of recovering a Robin coefficient defined on some non-accessible part of the boundary from available data on another part of the boundary in the non-stationary Stokes system. We prove a Lipschitz stability estimate under the a priori assumption that the Robin coefficient lives in some compact and convex subset of a finite dimensional vectorial subspace of the set of continuous functions. To do so, we use a theorem proved by L. Bourgeois and which establishes Lipschitz stability estimates for a class of inverse problems in an abstract framework.
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@article{CRMATH_2013__351_13-14_527_0,
author = {Egloffe, Anne-Claire},
title = {Lipschitz stability estimate in the inverse {Robin} problem for the {Stokes} system},
journal = {Comptes Rendus. Math\'ematique},
pages = {527--531},
publisher = {Elsevier},
volume = {351},
number = {13-14},
year = {2013},
doi = {10.1016/j.crma.2013.06.010},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2013.06.010/}
}
TY - JOUR AU - Egloffe, Anne-Claire TI - Lipschitz stability estimate in the inverse Robin problem for the Stokes system JO - Comptes Rendus. Mathématique PY - 2013 SP - 527 EP - 531 VL - 351 IS - 13-14 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2013.06.010/ DO - 10.1016/j.crma.2013.06.010 LA - en ID - CRMATH_2013__351_13-14_527_0 ER -
%0 Journal Article %A Egloffe, Anne-Claire %T Lipschitz stability estimate in the inverse Robin problem for the Stokes system %J Comptes Rendus. Mathématique %D 2013 %P 527-531 %V 351 %N 13-14 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2013.06.010/ %R 10.1016/j.crma.2013.06.010 %G en %F CRMATH_2013__351_13-14_527_0
Egloffe, Anne-Claire. Lipschitz stability estimate in the inverse Robin problem for the Stokes system. Comptes Rendus. Mathématique, Tome 351 (2013) no. 13-14, pp. 527-531. doi : 10.1016/j.crma.2013.06.010. http://www.numdam.org/articles/10.1016/j.crma.2013.06.010/
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