A MATHEMATICAL JUSTIFICATION OF THE LOW-FREQUENCY HETEROGENEOUS TIME-HARMONIC MAXWELL EQUATIONS

Abstract

This paper deals with the low-frequency model for the time-harmonic Maxwell equations in a heterogeneous medium which behaves like a conductor in one part and a perfect insulator in the other. The model is justified comparing the solution with the one given by the high-frequency heterogeneous model. A bound for the norm of the difference in terms of the frequency is given. It is also proven that the solution of the heterogeneous problem is the limit of the solutions of problems in a conductor with conductivity that tends to zero in a part of the medium.