  The analysis and homogenization of a moving boundary problem for a highly
heterogeneous, periodic two-phase medium is considered. In this context, the
normal velocity governing the motion of the interface separating the two
competing phases is assumed to be prescribed. Parametrizing the boundary motion
via a height function, the so-called Direct Mapping Method is employed to
construct a coordinate transform characterizing the changes with respect to the
initial setup of the geometry. Utilizing this transform, well-posedness of the
problem is established. After characterizing the limit behavior (with respect
to the heterogeneity parameter $\varepsilon\to0$) of the functions related to
the transformation, the homogenized problem of the heterogeneous two-scale
problem is deduced.
