Stability estimates for a Robin coefficient in the two-dimensional Stokes system

Muriel Boulakia; Anne-Claire Egloffe; Céline Grandmont

doi:10.3934/mcrf.2013.3.21

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2013, Volume 3, Issue 1: 21-49. Doi: 10.3934/mcrf.2013.3.21

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Stability estimates for a Robin coefficient in the two-dimensional Stokes system

1.
Université Pierre et Marie Curie-Paris 6, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris
2.
INRIA, Projet REO, Rocquencourt, BP 105, 78153 Le Chesnay cedex

Received: January 31, 2012

Revised: September 30, 2012

Published: February 2013

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Abstract

In this paper, we consider the Stokes equations and we are concerned with the inverse problem of identifying a Robin coefficient on some non accessible part of the boundary from available data on the other part of the boundary. We first study the identifiability of the Robin coefficient and then we establish a stability estimate of logarithm type thanks to a Carleman inequality due to A. L. Bukhgeim [11] and under the assumption that the velocity of a given reference solution stays far from $0$ on a part of the boundary where Robin conditions are prescribed.

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Mathematics Subject Classification: Primary: 35B35, 35R30; Secondary: 76D07.

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