On the Uniqueness Theorem of Time-Harmonic Electromagnetic Fields

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.

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.

Keywords

Time-Harmonic Fields, The Existence and Uniqueness of Solution, the Case of Lossless Medium, Operator Equation, Variational Principles, Weak Solution, Coercive Condition

Time-Harmonic Fields, The Existence and Uniqueness of Solution, the Case of Lossless Medium, Operator Equation, Variational Principles, Weak Solution, Coercive Condition

Cite this paper

nullY. Gui and P. Li, "On the Uniqueness Theorem of Time-Harmonic Electromagnetic Fields,"*Journal of Electromagnetic Analysis and Applications*, Vol. 3 No. 1, 2011, pp. 13-21. doi: 10.4236/jemaa.2011.31003.

nullY. Gui and P. Li, "On the Uniqueness Theorem of Time-Harmonic Electromagnetic Fields,"

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