  Inverse Stefan problem arising in modeling of laser ablation of biomedical
tissues is analyzed, where information on the coefficients, heat flux on the
fixed boundary, and density of heat sources are missing and must be found along
with the temperature and free boundary. Optimal control framework is employed,
where the missing data and the free boundary are components of the control
vector, and optimality criteria are based on the final moment measurement of
the temperature and position of the free boundary. Discretization by finite
differences is pursued, and convergence of the discrete optimal control
problems to the original problem is proven.
