  A simple multifractal coarsening model is suggested that can explain the
observed dynamical behavior of the fractal dimension in a wide range of
coarsening fractal systems. It is assumed that the minority phase (an ensemble
of droplets) at $t=0$ represents a non-uniform recursive fractal set, and that
this set is a geometrical multifractal characterized by a $f(\alpha)$-curve. It
is assumed that the droplets shrink according to their size and preserving
their ordering. It is shown that at early times the Hausdorff dimension does
not change with time, whereas at late times its dynamics follow the $f(\alpha)$
curve. This is illustrated by a special case of a two-scale Cantor dust. The
results are then generalized to a wider range of coarsening mechanisms.
