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Mathematics > Analysis of PDEs

arXiv:1810.07974 (math)
[Submitted on 18 Oct 2018 (v1), last revised 14 Aug 2020 (this version, v2)]

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

Authors:Dirk Pauly, Rainer Picard, Sascha Trostorff, Marcus Waurick
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Abstract: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.
Comments: 43 pages, additional remarks and references included; referees' comments incorporated
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph)
MSC classes: 35Q61, 35M12, 35M32, 35K65, 35K90, 35L90
Cite as: arXiv:1810.07974 [math.AP]
  (or arXiv:1810.07974v2 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1810.07974

Submission history

From: Marcus Waurick [view email]
[v1] Thu, 18 Oct 2018 09:48:25 UTC (30 KB)
[v2] Fri, 14 Aug 2020 08:56:26 UTC (35 KB)
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