KFU. Card publication. A new approach to investigation of Maxwell equations in spherical coordinates

KAZAN
FEDERAL UNIVERSITY

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A NEW APPROACH TO INVESTIGATION OF MAXWELL EQUATIONS IN SPHERICAL COORDINATES

Form of presentation

Articles in Russian journals and collections

Year of publication

2015

Authors, employees of KFU

Pleshhinskiy Nikolay Borisovich, author

Tumakov Dmitriy Nikolaevich, author

Bibliographic description in the original language

Pleshchinskii N.B., Tumakov D.N. A new approach to investigation of Maxwell equations in spherical coordinates // Lobachevskii Journal of Mathematics. – 2015. – Vol. 36, No. 1. – P. 15–27.

Annotation

In this article general solution to the Maxwell equations in spherical coordinates is constructed. The method of expansion of unknown functions into series of spherical harmonics is used. It is shown that the exterior boundary value problems for the Maxwell equations have the unique oriented solutions, and the interior boundary value problems have non-trivial solutions in the case of resonance. Necessary and sufficient solvability conditions of over-determined boundary value problems for the Maxwell equations are found.

Keywords

Maxwell set of equations, spherical coordinates, over-determined boundary value problem

The name of the journal

Lobachevskii J. Math.

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=98528&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Pleshhinskiy Nikolay Borisovich	ru_RU
dc.contributor.author	Tumakov Dmitriy Nikolaevich	ru_RU
dc.date.accessioned	2015-01-01T00:00:00Z	ru_RU
dc.date.available	2015-01-01T00:00:00Z	ru_RU
dc.date.issued	2015	ru_RU
dc.identifier.citation	Pleshchinskii N.B., Tumakov D.N. A new approach to investigation of Maxwell equations in spherical coordinates // Lobachevskii Journal of Mathematics. – 2015. – Vol. 36, No. 1. – P. 15–27.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=98528&p_lang=2	ru_RU
dc.description.abstract	Lobachevskii J. Math.	ru_RU
dc.description.abstract	In this article general solution to the Maxwell equations in spherical coordinates is constructed. The method of expansion of unknown functions into series of spherical harmonics is used. It is shown that the exterior boundary value problems for the Maxwell equations have the unique oriented solutions, and the interior boundary value problems have non-trivial solutions in the case of resonance. Necessary and sufficient solvability conditions of over-determined boundary value problems for the Maxwell equations are found.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Maxwell set of equations	ru_RU
dc.subject	spherical coordinates	ru_RU
dc.subject	over-determined boundary value problem	ru_RU
dc.title	A new approach to investigation of Maxwell equations in spherical coordinates	ru_RU
dc.type	Articles in Russian journals and collections	ru_RU