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Comptes Rendus Mathématique
Volume 351, n° 13-14
pages 527-531 (juillet 2013)
Doi : 10.1016/j.crma.2013.06.010
Received : 21 Mars 2013 ;  accepted : 28 June 2013
Lipschitz stability estimate in the inverse Robin problem for the Stokes system
Estimation de stabilité lipschitzienne de coefficients de Robin pour le système de Stokes
 

Anne-Claire Egloffe
 Projet Poems, Ensta-Paristech, 828, boulevard des Maréchaux, 91762 Palaiseau cedex, France 

Abstract

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.

The full text of this article is available in PDF format.
Résumé

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.

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