On the Resolution of an Inverse Problem by Shape Optimization Techniques

Abstract

In this work, we want to detect the shape and the location of an inclusion $\omega$ via some boundary measurement on $\partial \mathrm{\Omega }$. In practice, the body $\omega$ is immersed in a fluid flowing in a greater domain $\mathrm{\Omega }$ 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.