Uniqueness of the solution of initial-boundary value problem for the system of Maxwell’s equations in the quasistationary approximation for a nonmagnetic conductive body with non-smooth boundries

Author(s):  S.V.Marvin, candidate of Sciences, associate Professor, Ural Federal University named after the first President of Russia B.N. Yeltsin , Yekaterinburg, Russia, s.v.marvin@yandex.ru

Issue:  Volume 50, № 2

Rubric:  Physics. Mathematical modeling

Annotation:  An initial-boundary value problem of electrodynamics in neglect of the displacement current for a non-magnetic conductor, which is locating in a field of external current, are investigated. The statement of the problem does not assume a steady-state harmonic mode. It is assumed, that the boundary of conductor has points of nonsmoothness; it is assumed, that the every point of nonsmoothness may be point of edge or point of vertice (zero angles are possible). It is assumed, that the tensions of field are smooth vector func-tions in the separate mediums, their curls may be continuous extension to the boundaries of mediums, their tangent components are continuous when crossing the boundaries of mediums and their behavior at infinity is natural: the tension of electric field asymptotically does not exceed a function, inversely pro-portional the distance from the origin; the tension of magnetic field asymptotically does not exceed a function, inversely proportional the square of distance from the origin. About domain, external to the conductor, it is assumed, that it’s structure is surface-simply-connected. With all this assumptions it is proved, that the considered initial-boundary value problem has none more unique solution.

Keywords:  initial-boundary value problem, Maxwell’s equations, quasi-stationary approximation, exist-ence theorem, integro-differential equations.

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