  This paper analyses the well-posedness and properties of the extended
play-type model which was proposed in [van Duijn & Mitra (2018)] to incorporate
hysteresis in unsaturated flow through porous media. The model, when
regularised, reduces to a nonlinear degenerate parabolic equation coupled with
an ordinary differential equation. This has an interesting mathematical
structure which, to our knowledge, still remains unexplored. The existence of
solutions for the non-degenerate version of the model is shown using the
Rothe's method. An equivalent to maximum principle is proven for the solutions.
Existence of solutions for the degenerate case is then shown assuming that the
initial condition is bounded away from the degenerate points. Finally, it is
shown that if the solution for the unregularised case exists, then it is
contained within physically consistent bounds.
