Initial velocity of the emerging free boundary in a two-phase Stefan problem with imposed flux

The one dimensional, two phase Stefan problem with an imposed flux in which the phase change front originates at the material boundary was considered. It is proven that, subject to suitable assumptions on the initial temperature and imposed flux, the initial speed of the phase change front is equal to the jump between the surface and initial fluxes at the boundary. Similarly, it is shown that the front X(t) is continuously differentiable in the closed interval (0,t*) for some t* more than 0.