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The dynamical 3-dimensional inverse problem for the Maxwell system


Author: M. N. Demchenko
Translated by: the author
Original publication: Algebra i Analiz, tom 23 (2011), nomer 6.
Journal: St. Petersburg Math. J. 23 (2012), 943-975
MSC (2010): Primary 35R30
Published electronically: September 17, 2012
MathSciNet review: 2962180
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Abstract: The problem of recovering the scalar electric permittivity and magnetic permeability (respectively, $ \varepsilon $ and $ \mu $) of a medium in a bounded domain $ \Omega \subset {\mathbb{R}}^3$ by the boundary measurements on $ \partial \Omega $ is considered. As data, the value of the velocity $ c=(\varepsilon \mu )^{-1/2}$ with its normal derivative on $ \partial \Omega $ is taken, along with the response operator, which maps the tangential part $ e_\theta \mid _{\partial \Omega \times [0,2T]}$ of the electric field on the boundary to the tangential part $ h_\theta \mid _{\partial \Omega \times [0,2T]}$ of the magnetic field ($ 2T$ is the duration of measurements). With the help of the BC-method, it is established that the described data uniquely determine $ \varepsilon $ and $ \mu $ in the near-boundary layer with optical thickness $ T$, provided that the domain satisfies some geometric condition.


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Additional Information

M. N. Demchenko
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
Email: demchenko@pdmi.ras.ru

DOI: https://doi.org/10.1090/S1061-0022-2012-01224-0
Keywords: Inverse problem, Maxwell system, BC-method
Received by editor(s): December 20, 2010
Published electronically: September 17, 2012
Additional Notes: Supported by RFBR (grant no. 11-01-00407-a)
Dedicated: To the memory of my father, N. P. Demchenko
Article copyright: © Copyright 2012 American Mathematical Society