Problem of determining the permittivity in the stationary system of Maxwell equations
- 作者: Romanov V.1
-
隶属关系:
- Sobolev Institute of Mathematics, Siberian Branch
- 期: 卷 95, 编号 3 (2017)
- 页面: 230-234
- 栏目: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225049
- DOI: https://doi.org/10.1134/S1064562417030164
- ID: 225049
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详细
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.
作者简介
V. Romanov
Sobolev Institute of Mathematics, Siberian Branch
编辑信件的主要联系方式.
Email: romanov@math.nsc.ru
俄罗斯联邦, Novosibirsk, 630090