We present an abstract framework for parabolic type equations which possibly degenerate on certain spatial regions. The degeneracies are such that the equations under investigation may admit a type change ranging from parabolic to elliptic type problems. The approach is an adaptation of the concept of so-called evolutionary equations in Hilbert spaces and is eventually applied to a degenerate eddy current type model. The functional analytic setting requires quite minimal assumptions on the boundary and interface regularity. The degenerate eddy current model is justified as a limit model of non-degenerate hyperbolic models of Maxwell's equations.

中文翻译：

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一类退化抽象抛物线问题及其在涡流模型中的应用

我们为可能在某些空间区域退化的抛物线型方程提出了一个抽象框架。简并性使得正在研究的方程可能允许从抛物线型问题到椭圆型问题的类型变化。该方法是对希尔伯特空间中所谓的进化方程概念的改编，最终应用于退化涡流类型模型。功能分析设置对边界和界面规律性的假设非常少。简并涡流模型被证明是麦克斯韦方程组非简并双曲模型的极限模型。