Initial-boundary value problem of electromagnetic testing of a flawed ferromagnetic conductor by the residual field of an instantaneously cut-off current

Abstract

An initial-boundary value problem of electrodynamics is considered for a flawed metal ferromagnetic body that is placed in the field of an instantaneously cut-off extraneous current. A generalized statement of the problem has been found that guarantees the uniqueness of solution and its continuous dependence on the initial data under fairly sweeping assumptions about the conductivity and permeability of the body as well as the smoothness of boundaries of the body and the flaws. Possible generalizations are pointed out for the results to include ferromagnetic conducting bodies that are placed in the field of permanently switched-on current.