Abstract
The initial-boundary value problem for the quasi-stationary magnetic approximation of the time-dependent Maxwell equations with magnetic boundary conditions is studied. The case of inhomogeneous media containing conductive and non-conductive inclusions is considered. The problem is reduced to the problems of determining vector magnetic and scalar electric potentials. The special gauges are used, that generalize the Coulomb and Lorenz gauges and allow to formulate the problems of the independent definitions of the vector magnetic potential. The correctness of the problems are established under general conditions on the coefficients. The relation between solutions of the problems with different gauges is studied. The equivalence of the problems for potentials to the original boundary value problem is proved.
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