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Bibliographic description:
Marvin S. V.
INITIAL BOUNDARY VALUE PROBLEM OF ELECTRODYNAMICS FOR A DEFECTIVE FERRITE BODY // BSU bulletin. Mathematics, Informatics. - 2019. №1. . - С. 31-40.
Title:
INITIAL BOUNDARY VALUE PROBLEM OF ELECTRODYNAMICS FOR A DEFECTIVE FERRITE BODY
Financing:
Codes:
DOI: 10.18101/2304-5728-2019-1-31-40UDK: 517.968.73
Annotation:
The article considers initial boundary value problem for Maxwell's equations in re- lation to a ferrite body, which has some structural defects. For initial boundary value problem we have chosen a functional class that takes into account the matching conditions on the interface of two media, which are not perfect conductors. Vector fields of this functional class are square-integrable in the whole space and have square-integrable generalized rotors. In addition, vector fields are time- differentiable in the sense of convergence in mean-square norm. Operating with broad assumptions about the dependence of electrical conductivity, dielectric and magnetic permeability of a ferrite on spaces coordinates, and natural assumptions about the dependence of external current on time, it has been shown, that in the given functional class there is one and only one solution of the considered initial boundary value problem, and that solution is continuous in the initial conditions.

Keywords:
Maxwell’s equations; initial conditions; matching conditions; mean- square norm; Banach space; existence theorem; generalized rotor; integro- differential equations; closed operator; inverse operator.
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