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An inverse boundary value problem for the Oseen equation
Author(s) -
Kress Rainer,
Meyer Sascha
Publication year - 2000
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(20000125)23:2<103::aid-mma106>3.0.co;2-4
Subject(s) - mathematics , uniqueness , mathematical analysis , boundary value problem , differentiable function , inverse problem , obstacle , integral equation , boundary (topology) , political science , law
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 Fréchet 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. Copyright © 2000 John Wiley & Sons, Ltd.