Тип публикации: статья из журнала
Год издания: 2011
Идентификатор DOI: 10.1134/S0037446611020030
Ключевые слова: energy functional, elliptic equation, electrodynamics
Аннотация: We propose some minimum principle for an energy functional in an elliptic boundary value problem that arises in constructing time-harmonic solutions to the Maxwell equations. We suggest the potentials other than the vector and scalar potentials, used in the mathematical modeling of electromagnetic fields since the operators of tradПоказать полностьюitional problems are not sign definite, which complicates constructions of iterative solution methods. We consider the problem in a parallelepiped whose boundary is ideally conducting. For nonresonant frequencies we prove that the operator of the boundary value problem is positive definite, propose a minimum principle for a quadratic energy functional, and prove the existence and uniqueness of generalized solutions.
Журнал: SIBERIAN MATHEMATICAL JOURNAL
Выпуск журнала: Vol. 52, Is. 2
Номера страниц: 207-221
ISSN журнала: 00374466
Место издания: NEW YORK
Издатель: CONSULTANTS BUREAU/SPRINGER