  We present an application of recent well-posedness results in the theory of
delay differential equations for ordinary differential equations
arXiv:2308.04730 to a generalized population model for stem cell maturation.
The weak approach using Sobolev-spaces we take allows for a larger class of
initial prehistories and makes checking the requirements for well-posedness of
such a model considerably easier compared to previous approaches. In fact the
present approach is a possible means to guarantee that the solution manifold is
not empty, which is a necessary requirement for a $C^{1}$-approach to work.
