Problem of Determining the Anisotropic Conductivity in Electrodynamic Equations

V. G. Romanov

Research output: Contribution to journalArticlepeer-review

Abstract

For a system of electrodynamic equations, the inverse problem of determining an anisotropic conductivity is considered. It is supposed that the conductivity is described by a diagonal matrix (Formula presented.) outside of the domain (Formula presented.), and the permittivity ε and the permeability μ of the medium are positive constants everywhere in (Formula presented.). Plane waves coming from infinity and impinging on an inhomogeneity localized in Ω are considered. For the determination of the unknown functions (Formula presented.), and (Formula presented.), information related to the vector of electric intensity is given on the boundary S of the domain Ω. It is shown that this information reduces the inverse problem to three identical problems of X-ray tomography.

Original languageEnglish
Article number11
Pages (from-to)44-46
Number of pages3
JournalDoklady Mathematics
Volume103
Issue number1
DOIs
Publication statusPublished - Jan 2021

Keywords

  • anisotropy
  • conductivity
  • inverse problem
  • Maxwell equations
  • plane waves
  • tomography

OECD FOS+WOS

  • 1.01 MATHEMATICS

State classification of scientific and technological information

  • 27 MATHEMATICS

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