On a class of degenerate abstract parabolic problems and applications to some eddy current models

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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.


Original languageEnglish
Article number108847
Number of pages45
JournalJournal of functional analysis
Issue number7
Early online dateFeb 2021
Publication statusPublished - 1 Apr 2021

External IDs

ORCID /0000-0003-4155-7297/work/145224259
WOS 000615710700010


ASJC Scopus subject areas


  • Eddy current model, Evo-systems, Evolutionary equations, Helmholtz decomposition, Maxwell's equations, Mixed type equations