An initial-boundary value problem of structurescopy of a nonferromagnetic metal solid with foreign dielectric inclusions using the residual field of an instantaneously cut-off extraneous current

Abstract

An initial-boundary value problem of electrodynamics is considered for the structurescopy of a nonferromagnetic metal with foreign dielectric inclusions; it is assumed that structurescopy is carried out using the residual electromagnetic field of an instantaneously cut-off extraneous current. Under the fairly sweeping assumptions on the electric conductivity of the solid, the dielectric permittivity of the foreign inclusions, and the smoothness of the boundaries of the solid and the inclusions, it has been proven that the initial-boundary value problem of electrodynamics under consideration has a unique solution, which depends continuously on the initial conditions.