  We assume that the Stefan problem with undercooling has a classical solution
until the moment of contact of free boundaries and the free boundaries have
finite velocities until the contact. Under these assumptions, we construct a
smooth approximation of the global solution of the Stefan problem with
undercooling, which, until the contact, gives the classical solution mentioned
above and, after the contact, gives a solution which is the solution of the
heat conduction equation.
