Uniqueness and stable determination in the inverse Robin transmission problem with one electrostatic measurement |
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Authors: | Z. Belhachmi H. Meftahi |
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Affiliation: | 1. Mathematics, Information Technology and Applications Laboratory, Mulhouse Cedex, France;2. Technische Universit?t Berlin, Berlin, Germany |
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Abstract: | In this paper, we consider the inverse Robin transmission problem with one electrostatic measurement. We prove a uniqueness result for the simultaneous determination of the Robin parameter p, the conductivity k, and the subdomain D, when D is a ball. When D and k are fixed, we prove a uniqueness result and a directional Lipschitz stability estimate for the Robin parameter p. When p and k are fixed, we give an upper bound to the subdomain D. For the reconstruction purposes of the Robin parameter p, we set the inverse problem under an optimization form for a Kohn–Vogelius cost functional. We prove the existence and the stability of the optimization problem. Finally, we show some numerical experiments that agree with the theoretical considerations. Copyright © 2013 John Wiley & Sons, Ltd. |
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Keywords: | inverse problems integral equations uniqueness stability identification |
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