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On the resolution of an inverse problem by shape optimization techniques. (English) Zbl 1474.76025

Summary: In this work, we want to detect the shape and the location of an inclusion \(\omega\) via some boundary measurement on \(\partial\Omega\). In practice, the body \(\omega\) is immersed in a fluid flowing in a greater domain \(\Omega\) and governed by the Stokes equations. We study the inverse problem of reconstructing \(\omega\) using shape optimization methods by defining the Kohn-Vogelius cost functional. We aim to study the inverse problem with Neumann and mixed boundary conditions.

MSC:

76D55 Flow control and optimization for incompressible viscous fluids
65J22 Numerical solution to inverse problems in abstract spaces
49Q10 Optimization of shapes other than minimal surfaces
76D07 Stokes and related (Oseen, etc.) flows
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