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

Muriel Boulakia (1, 2) , Anne-Claire Egloffe (2) , Céline Grandmont (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 REO - Numerical simulation of biological flows

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 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.

Mots clés: Logarithmic stability estimate; Inverse boundary coefficient problem; Stokes system; Robin boundary condition; Identifiability; Carleman inequality; Logarithmic stability estimate.

Domaines: Equations aux dérivées partielles [math.AP]

Muriel Boulakia, Anne-Claire Egloffe, Céline Grandmont. Stability estimates for a Robin coefficient in the two-dimensional Stokes system. Mathematical Control and Related Fields, 2013, 3 (1), https://www.aimsciences.org/journals/pdfs.jsp?paperID=8296&mode=full. ⟨hal-00582559v3⟩