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An inverse boundary value problem for the Oseen equation

✍ Scribed by Rainer Kress; Sascha Meyer

Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
157 KB
Volume
23
Category
Article
ISSN
0170-4214

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✦ Synopsis

Based on the two-dimensional stationary Oseen equation we consider the problem to determine the shape of a cylindrical obstacle immersed in a #uid #ow from a knowledge of the #uid 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 "rst kind. For a foundation of Newton-type methods we establish the FreH chet di!erentiability 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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