Abstract
Based on the two-dimensional stationary Oseen equation we consider the problem to determine the shape of a cylindrical obstacle immersed in a fluid flow from a knowledge of the fluid velocity on some arc outside the obstacle. First, we obtain a uniqueness result for this ill-posed and non-linear inverse problem. Then, for the approximate solution we propose a regularized Newton iteration scheme based on a boundary integral equation of the first kind. For a foundation of Newton-type methods we establish the Frechet differentiability of the solution to the Dirichlet problem for the Oseen equation with respect to the boundary and investigate the injectivity of the linearized mapping. Some numerical examples for the feasibility of the method are presented.
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