Solution of the Cauchy Problem for the Three-Dimensional Telegraph Equation and Exact Solutions of Maxwell’s Equations in a Homogeneous Isotropic Conductor with a Given Exterior Current Source

Akhmetov, O.I.; Mingalev, V.S.; Mingalev, I.V.; Mingalev, O.V.

Авторы: Akhmetov O.I., Mingalev V.S., Mingalev I.V., Mingalev O.V.
Журнал: Computational Mathematics and Mathematical Physics
Том: 58
Номер: 4
Год издания: 2018
Издательство: Pleiades Publishing, Ltd
Местоположение издательства: Road Town, United Kingdom
Первая страница: 604
Последняя страница: 611
Оригинальные версии: РЕШЕНИЕ ЗАДАЧИ КОШИ ДЛЯ ТРЕХМЕРНОГО ТЕЛЕГРАФНОГО УРАВНЕНИЯ И ТОЧНЫЕ РЕШЕНИЯ УРАВНЕНИЙ МАКСВЕЛЛА В ОДНОРОДНОМ ИЗОТРОПНОМ ПРОВОДНИКЕ С ЗАДАННЫМ ИСТОЧНИКОМ ВНЕШНЕГО ТОКА
DOI: 10.1134/s0965542518040036
Аннотация: For the solution of the Cauchy problem for the linear telegraph equation in three-dimensional space, we derive a formula similar to the Kirchhoff one for the linear wave equation (and turning into the latter at zero conductivity). Additionally, the problem of determining the field of a given exterior current source in an infinite homogeneous isotropic conductor is reduced to a generalized Cauchy problem for the three-dimensional telegraph equation. The derived formula enables us to reduce this problem to quadratures and, in some cases, to obtain exact three-dimensional solutions with a propagating front, which are of great applied importance for testing numerical methods for solving Maxwell's equations. As an example, we construct the exact solution of the field from a Hertzian dipole with an arbitrary time dependence of the current in an infinite homogeneous isotropic conductor.
Добавил в систему: Ахметов Олег Иршатович

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Solution of the Cauchy Problem for the Three-Dimensional Telegraph Equation and Exact Solutions of Maxwell’s Equations in a Homogeneous Isotropic Conductor with a Given Exterior Current Sourceстатья