TITLE:
On the Uniqueness Theorem of Time-Harmonic Electromagnetic Fields
AUTHORS:
Yongfeng Gui, Pei Li
KEYWORDS:
Time-Harmonic Fields, The Existence and Uniqueness of Solution, the Case of Lossless Medium, Operator Equation, Variational Principles, Weak Solution, Coercive Condition
JOURNAL NAME:
Journal of Electromagnetic Analysis and Applications,
Vol.3 No.1,
January
21,
2011
ABSTRACT: The uniqueness theorem of time-harmonic electromagnetic fields, which is the theoretical basis of boundary value problem (BVP) of electromagnetic fields, is reviewed. So far there are many versions of the statements and proofs on the theorem. However, there exist some limitations and lack of strictness in these versions, for instance, the discussion of the uniqueness of solution without considering the existence of solution and the lack of strictness in the case of loss-less medium. In contrast with the traditional statements and proofs, this paper introduces some important conclusions on operator equation from modern theory of partial differential equation (PDE) and attempts to solve the problems on the existence and uniqueness of the solution to operator equation which is derived from Maxwell’s equations of time-harmonic electromagnetic fields. This method provides a novel and rigorous approach to discuss and solve the existence and uniqueness of the solution to time- harmonic fields in the new mathematical framework. Some important conclusions are presented.