麦克斯韦方程组的初边值问题
Formulating Initial and Boundary Effects for Maxwell Equations
摘要：
在麦克斯韦方程组的经典处理中，初始和边界条件的引入是通过数学考虑，而不是严格使用麦克斯韦方程组。结果，初始和边界条件与麦克斯韦方程组在逻辑上不一致。实际上，经典麦克斯韦方程组的边值问题在一般情况下是不可解的，只要给定整个边界场。这个问题是由于在引入边界条件时隐含了向量的散度和旋度没有关系而引起的。这项研究引入了新的想法和配方来解决这个问题。研究表明，基于秩为2的张量的Chen S-R分解，可以消除这种逻辑上的不一致性，从而重构经典的麦克斯韦方程组.根据重新表述的麦克斯韦方程组，初始条件和边界条件具有全局效应。作为例子，推导了超导体的伦敦方程.
英文摘要：
In classical treatment of Maxwell equations, the initial and boundary conditions are introduced by mathematical consideration rather than strictly using the Maxwell equations. As a result, the initial and boundary conditions are not logic consistent with the Maxwell equations. In fact, the boundary problem of classical Maxwell equations is not solvable for general cases, if the whole boundary fields are given. This problem is caused by implying the divergence and the curl of a vector have no relations during introducing the boundary condition. This research introduces new ideas and formulations to solve this problem. The research shows that based on Chen S-R decomposition of a rank-two tensor, this logical un-consistency can be discarded and, as a consequence, the classical Maxwell equations are reformulated. According to the reformulated Maxwell equations, the initial condition and boundary condition have global effects. As an example, the London equations for superconductors are deduced.
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