  Domain decomposition based time integrators allow the usage of parallel and
distributed hardware, making them well-suited for the temporal discretization
of parabolic systems, in general, and degenerate parabolic problems, in
particular. The latter is due to the degenerate equations' finite speed of
propagation. In this study, a rigours convergence analysis is given for such
integrators without assuming any restrictive regularity on the solutions or the
domains. The analysis is conducted by first deriving a new variational
framework for the domain decomposition, which is applicable to the two standard
degenerate examples. That is, the $p$-Laplace and the porous medium type vector
fields. Secondly, the decomposed vector fields are restricted to the underlying
pivot space and the time integration of the parabolic problem can then be
interpreted as an operators splitting applied to a dissipative evolution
equation. The convergence results then follow by employing elements of the
approximation theory for nonlinear semigroups.
