Problems of determining quasi-stationary electromagnetic fields in weakly inhomogeneous media

Formulations of initial-boundary value problems for the system of Maxwell’s equations in various quasi-stationary approximations in homogeneous and inhomogeneous conducting media are considered. In the case of weakly inhomogeneous media, asymptotic expansions of solutions to the considered initial-boundary value problems in a parameter characterizing the degree of inhomogeneity of the medium are formulated and substantiated. It is shown that the construction of an asymptotic expansion for the quasi-stationary electromagnetic approximation leads to successively solving independent problems for the quasi-stationary electric and quasi-stationary magnetic approximations in a homogeneous medium. Conditions for the initial data providing the convergence of the asymptotic series are given.