PROBLEMS OF DETERMINING QUASI-STATIONARY ELECTROMAGNETIC FIELDS IN WEAKLY INHOMOGENEOUS MEDIA

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Abstract

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.

About the authors

A. V. Kalinin

National Research Lobachevsky State University of Nizhny Novgorod; Institute of Applied Physics, Russian Academy of Sciences

Email: avk@mm.unn.ru
Nizhny Novgorod, 603022 Russia; Nizhny Novgorod, 603950 Russia

A. A. Tyukhtina

National Research Lobachevsky State University of Nizhny Novgorod

Email: tyukhtina@iee.unn.ru
Nizhny Novgorod, 603022 Russia

S. A. Malov

National Research Lobachevsky State University of Nizhny Novgorod

Nizhny Novgorod, 603022 Russia

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