ABSTRACT

The $\mathbf{\text{A}}-\phi -\mathbf{\text{B}}$ magnetodynamic Maxwell system given in its potential and space-time formulation is a popular model considered in the engineering community. It allows to model some phenomena such as eddy current losses in multiple turn winding. Indeed, in some cases, they can significantly alter the performance of the devices, and consequently can no more be neglegted. It turns out that this model is not yet analytically studied, therefore we here consider its well-posedness. First, the existence of strong solutions with the help of the theory of Showalter on degenerated parabolic problems is established. Second, using energy estimates, existence and uniqueness of the weak solution of the $\mathbf{\text{A}}-\phi -\mathbf{\text{B}}$ is deduced.

摘要

这$\mathbf{\text{一个}}-\phi -\mathbf{\text{乙}}$在其势和时空公式中给出的磁动力麦克斯韦系统是工程界考虑的流行模型。它允许对一些现象进行建模，例如多匝绕组中的涡流损耗。事实上，在某些情况下，它们可以显着改变设备的性能，因此不能再被忽视。事实证明，这个模型还没有经过分析研究，因此我们在这里考虑它的适定性。首先，借助Showalter关于退化抛物线问题的理论，建立了强解的存在性。二、利用能量估计，弱解的存在性和唯一性$\mathbf{\text{一个}}-\phi -\mathbf{\text{乙}}$被推导出来。