On the Uniqueness Theorem of Time-Harmonic Electromagnetic Fields

Yongfeng Gui, Pei Li
2011 Journal of Electromagnetic Analysis and Applications  
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 lossless medium. In contrast
more » ... ith 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. On the Uniqueness Theorem of Time-Harmonic Electromagnetic Fields 6.2.2. The Further Discussion on the Solution to Helmholtz Equation Although the Lax-Milgram theo oincare inequa in the proce rem plays a very impormeri-J tant role in the solving of the weak solution and nu
doi:10.4236/jemaa.2011.31003 fatcat:k255fuvwcjephgt5n6pwt6gjwa