麦克斯韦方程组超定问题的解释  

COMMENTS ON OVER-DETERMINATION OF MAXWELL'S EQUATIONS

作　　者：刘长礼[1] 

机构地区：[1]北京应用物理与计算数学研究所,北京100094

出　　处：《物理与工程》2017年第3期7-9,21,共4页Physics and Engineering

摘　　要：麦克斯韦方程组有6个未知量,8个方程,是超定方程组.对于超定问题一般这样解释:认为两个散度方程是不独立的,只需初始时刻满足即可,之后自动满足。所以计算电磁学中只求解旋度方程,而不求解散度方程。文中指出这种解释有一个循环逻辑缺陷,从而导致此种解释不正确;在计算电磁学中两个散度方程必须求解。推广的线性相关概念用以解释偏微分方程超定问题。在这个推广的线性相关定义下,原来众多"表面"超定方程都变成了适定方程,避免了一些歧义。Maxwell＇s equations seem over determined, which have six unknowns and eight equations. It is generally believed that Maxwell＇s divergence equations are redundant, and both equations are thought as initial conditions of curl ones. Because of this explanation, two divergence equations usually are not solved in computational electromagnetics. A circular logical fallacy of this explanation is found, and two divergence equations cannot be ignored in compu- tational electromagnetics, which are not redundant, but fundamental. The definition of differential linear dependence is employed to explain over-determination of Maxwell＇s equations. In the generalized definition, several overdetermined equations become well-determined ones, which avoid some ambiguity. This paper in English can be referred to arXiv. 1002. 0892.

关 键 词：麦克斯韦方程组 超定 散度 

分 类 号：O175[理学—数学]