  We study self-similar solutions of a multi-phase Stefan problem, first in the
case of one space variable, and then in the radial multidimensional case. In
both these cases we prove that a nonlinear algebraic system for determination
of the free boundaries is gradient one and the corresponding potential is an
explicitly written coercive function. Therefore, there exists a minimum point
of the potential, coordinates of this point determine free boundaries and
provide the desired solution. Moreover, in one-dimensional case the potential
is proved to be strictly convex and this implies the uniqueness of the
solution. In contrary, in the multidimensional case the potential is not convex
but the uniqueness of our solution remains true, it follows from the general
theory. Bibliography: 3 titles.
