On determination of the permittivity through the module of the vector of the electric strength of the high-frequency electromagnetic field

Cover Page

Abstract


For nonmagnetic and nonconductive medium the system of electrodynamic equations that corresponds to periodic in time oscillations is considered. An inverse problem of determining permittivity in this system by the given module of the electric strength is studied. It is supposed that the electric fields is a result of the interference of two fields created by point sources. The permittivity e(x) is assumed to be differ from a given positive constant e0 inside of a compact domain W0 Ì R3 only. An information on module of the electric strength is given on the boundary of the domain W contained W0 inside itself and for all frequencies beginning with some fixed frequency w0. The asymptotic behavior of solution of a direct problem related to the electrodynamic equations is studied and the original inverse problem is reduced to the well known inverse kinematic problem. This reduction open a way for constructive solution of the inverse phaseless problem.


V. G. Romanov

Институт математики им. С.Л. Соболева Сибирского отделения Российской Академии наук

Author for correspondence.
Email: romanov@math.nsc.ru

Russian Federation, Новосибирск

  1. Klibanov M.V., Romanov V.G. // J. Inverse and Ill­ Posed Problems. 2015. V. 23. № 4. P. 415–428.
  2. Klibanov M.V., Romanov V.G. // Eurasian J. Math. and Comput. Appl. 2015. V. 3. № 1. P. 48–63.
  3. Novikov R.G. // J. Geom. Anal. 2015. DOI: 10.1007/ 5.12220­014­9553­7.
  4. Novikov R.G. // Bull. Sci. Math. 2015. DOI: 10.1016/j. bulsci.2015.04.005.
  5. Klibanov M.V., Romanov V.G. // J. Inverse and Ill­ Posed Problems. 2015. V. 23. № 2. P. 187–193.
  6. Romanov V.G. // Eurasian J. Math. and Computer Appl. 2015. V. 3. № 4. P. 68–84.
  7. Klibanov M.V., Romanov V.G. // SIAM J. Appl. Math. 2016. V. 76. № 1. P. 178–196.
  8. Klibanov M.V., Romanov V.G. // Inverse Problems. 2016. V. 32. № 2. 015005 (16 pp). doi: 10.1088/0266­. 5611/32/1/015005.
  9. Klibanov M.V., Romanov V.G. // Inverse Problems. 2017. V. 33. № 9. 095007 (10 pp).
  10. Романов В.Г. // Сиб. мат. журн. 2017. Т. 58. № 4. С. 916–924.
  11. Романов В.Г. // ДАН. 2017. Т. 474. № 4. С. 413–417.
  12. Романов В.Г. // Сиб. мат. журн. 2018. Т. 59. № 3. С. 626–638.
  13. Мухометов Р.Г. // ДАН. 1977. Т. 232. № 1. С. 32–35.
  14. Мухометов Р.Г., Романов В.Г. // ДАН. 1978. Т. 243. № 1. С. 41–44.
  15. Бернштейн И.Н., Гервер М.Л. // ДАН. 1978. Т. 243. № 2. С. 302–305.

Views

Abstract - 14

PDF (Russian) - 34

PlumX


Copyright (c) 2019 Российская академия наук