A New Approach to Investigation of Maxwell Equations in Spherical Coordinates

被引：1

作者：

Pleshchinskii, N. B. ^{[1
]}

Tumakov, D. N. ^{[1
]}

机构：

[1] Kazan Fed Univ, Kazan, Russia

来源：

LOBACHEVSKII JOURNAL OF MATHEMATICS | 2015年 / 36卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

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

D O I：

10.1134/S1995080215010114

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：15 / 27

页数：13

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