The dynamical 3-dimensional inverse problem for the Maxwell system
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M. N. Demchenko
Translated by: the author - St. Petersburg Math. J. 23 (2012), 943-975
- DOI: https://doi.org/10.1090/S1061-0022-2012-01224-0
- Published electronically: September 17, 2012
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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.References
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Bibliographic 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
- Received by editor(s): December 20, 2010
- Published electronically: September 17, 2012
- Additional Notes: Supported by RFBR (grant no. 11-01-00407-a)
- © Copyright 2012 American Mathematical Society
- Journal: St. Petersburg Math. J. 23 (2012), 943-975
- MSC (2010): Primary 35R30
- DOI: https://doi.org/10.1090/S1061-0022-2012-01224-0
- MathSciNet review: 2962180
Dedicated: To the memory of my father, N. P. Demchenko