  We consider the optimal control of singular nonlinear partial differential
equation which is the distributional formulation of the multiphase Stefan type
free boundary problem for the general second order parabolic equation. Boundary
heat flux is the control parameter, and the optimality criteria consist of the
minimization of the $L_2$-norm declination of the trace of the solution to the
PDE problem at the final moment from the given measurement. Sequence of
finite-dimensional optimal control problems is introduced through finite
differences. We establish existence of the optimal control and prove the
convergence of the sequence of discrete optimal control problems to the
original problem both with respect to functional and control. Proofs rely on
establishing a uniform $L_{\infty}$ bound, and $W_2^{1,1}$-energy estimate for
the discrete nonlinear PDE problem with discontinuous coefficient.
