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.
|Number of pages
|Journal of functional analysis
|Early online date
|Published - 1 Apr 2021
ASJC Scopus subject areas
- Eddy current model, Evo-systems, Evolutionary equations, Helmholtz decomposition, Maxwell's equations, Mixed type equations