Lipschitz stability estimate for the Stokes system with Robin boundary conditions

Anne-Claire Egloffe (1)

1 REO - Numerical simulation of biological flows

In this research report, we study the inverse problem of identifying a Robin coefficient defined on some non accessible part of the boundary from measurements available on the other part of the boundary, for (u,p) solution of the Stokes system. We prove a Lipschitz stability estimate, under the a priori assumption that the Robin coefficient is piecewise constant. To do so, we use unique continuation estimates for the Stokes system proved in [BEG12] and the approach developed by E. Sincich in [Sin07] to solve a similar inverse problem for the Laplace equation.

Keywords: Lipschitz stability estimate; Inverse problem; Stokes system; Lipschitz stability estimate.

Domains: Analysis of PDEs [math.AP]

Anne-Claire Egloffe. Lipschitz stability estimate for the Stokes system with Robin boundary conditions. [Research Report] RR-8222, INRIA. 2012. ⟨hal-00788954⟩