Problems of Determining Quasi-Stationary Electromagnetic Fields in Weakly Inhomogeneous Media

Statements of initial-boundary value problems for the system of Maxwell 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 of the initial-boundary value problems under consideration 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 a quasi- stationary electromagnetic approximation leads to a sequential solution of independent problems for a quasi- stationary electric and quasi-stationary magnetic approximation in a homogeneous medium. Conditions on the initial data are given for which the asymptotic series are convergent.