Problem of determining the permittivity in the stationary system of Maxwell equations
- Authors: Romanov V.G.1
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Affiliations:
- Sobolev Institute of Mathematics, Siberian Branch
- Issue: Vol 95, No 3 (2017)
- Pages: 230-234
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225049
- DOI: https://doi.org/10.1134/S1064562417030164
- ID: 225049
Cite item
Abstract
The stationary system of Maxwell equations for a unmagnetized nonconducting medium is considered. For this system, the problem of determining the permittivity ε from given electric or magnetic fields is studied. It is assumed that the electromagnetic field is induced by a plane wave coming from infinity in the direction ν. It is also assumed that the permittivity is different from a given positive constant ε0 only inside a compact domain Ω ⊂ R3 with a smooth boundary S. To find ε inside Ω, the solution of the corresponding direct problem for the system of electrodynamic equations on the shadow portion of the boundary of Ω is specified for all frequencies starting at some fixed ω0 and for all ν. The high-frequency asymptotics of the solution to the direct problem is studied. It is shown that the information specified makes it possible to reduce the original problem to the well-known inverse kinematic problem of determining the refraction coefficient inside Ω from the traveling times of an electromagnetic wave. This leads to a uniqueness theorem for the solution of the problem under consideration and opens up the opportunity of its constructive solution.
About the authors
V. G. Romanov
Sobolev Institute of Mathematics, Siberian Branch
Author for correspondence.
Email: romanov@math.nsc.ru
Russian Federation, Novosibirsk, 630090