动态电磁场唯一性定理中的若干关键理论问题

Former description about the uniqueness theorem of electromagnetic fields is not perfect. Firstly, it doesn't concern characteristics of mediums. Secondly, the description about tangent interface conditions doesn't coincide with practical situation. Thirdly, according to the theorem, it is difficult to write out the formulation of electromagnetic field initial-boundary value problem directly. To solve these problems, this project studies the basic theory of electromagnetic field initial-boundary value problem and its analytic methods systematically. The uniqueness theorem of dynamic electromagnetic fields applying to linear multi-medium region and the uniqueness theorem of transient eddy current are gotten. On the basis of them, the analytical expression to impedance for the coil above conductive and permeable medium that have a variable permeability, and the analytical expression to inductance for the coil with ferrite core of finite length are derived. A monograph, Analytical methods for time-harmonic electromagnetic fields, which is published by Science Press and is supported by the Science Publication Foundation of CAS(the Chinese Academy of Sciences), includes some of these achievements. In addition, three papers on important publications, and two papers on other journals include other achievements. After searching many documents, it is found that all these achievements appear for the first time. These achievements have plenty of scientific significations. Firstly, according to new uniqueness theorem, the formulation of electromagnetic field initial-boundary value problem can be written out directly and blind try is avoided. Secondly, using the improved uniqueness theorem, the formulation of boundary value problem expressed by vector magnetic potential is simplified and the complexity in solving the problem is reduced. Thirdly, these achievements develop the basic theory of electromagnetic field boundary value problem.

以往表述的动态电磁场唯一性定理尚存不足：它没有限定媒质特性，对切向边界条件的描述与实际使用状况不符，难于根据该定理写出电磁场初边值问题表达式。本项目拟针对以上问题展开研究，探讨不同媒质中解的唯一性条件，并希望得到动态电磁场问题的初边值问题表达式。此项研究可进一步完善电磁场边值理论，在理论和应用上具有较大意义。