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

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

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.

Details

OriginalspracheEnglisch
Aufsatznummer108847
Seitenumfang45
FachzeitschriftJournal of functional analysis
Jahrgang280
Ausgabenummer7
Frühes Online-DatumFeb. 2021
PublikationsstatusVeröffentlicht - 1 Apr. 2021
Peer-Review-StatusJa

Externe IDs

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

Schlagworte

ASJC Scopus Sachgebiete

Schlagwörter

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