  Optimal control of the singular nonlinear parabolic PDE which is a
distributional formulation of multidimensional and multiphase Stefan-type free
boundary problem is analyzed. Approximating sequence of finite-dimensional
optimal control problems is introduced via finite differences. Existence of the
optimal control and the convergence of the sequence of discrete optimal control
problems both with respect to functional and control is proved. In particular,
convergence of the method of finite differences, and existence, uniqueness and
stability estimations are established for the singular PDE problem under
minimal regularity assumptions on the coefficients.
