Analytical solution of a non-smooth freezing front

Short-time analytical solution has been obtained for a non-smooth freezing front which develops when the temperature is prescribed over a finite length on the surface of a melt occupying a two-dimensional half space. An interesting feature of the solution is that at the ends of the finite length over which the solidification initiates, removable singularities occur which tend to limits which are consistent with the physics of the problem. The spreads along the surface have been obtained in a novel way from the solution of an auxiliary problem. The spread along the surface can have unusual growth rates. Some inverse problems have been discussed.