This problem description is taken from Illingworth and Golosnoy [1]: For physical systems of inhomogeneous composition, diusion is often observed to cause a change of phase, even in material held at a constant temperature. The concentration of one phase in contact with the other is generally fixed by a thermodynamic constraint. But the rate at which solute diuses towards the interface through phase A and the rate at which it is removed into phase B are not necessarily equal. In order to conserve solute, therefore, the interface between the two phases must move. Suppose that phase A exists for 0  r  s(t) and phase B exists for s(t)  r  R, where r is the spatial variable and s(t) denotes the position of the moving boundary.