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

On a Class of Degenerate Abstract Parabolic Problems and Applications to Some Eddy Current Models