Recovering the timewise reaction coefficient for a two-dimensional free boundary problem

The reconstruction of the timewise reaction and free boundary coefficients in the heat equation from an additional Stefan-type and mass/energy measurements data is considered. This inverse formulation results in a local uniquely solvable problem. The two-dimensional inverse problem is discretized using an alternating direction explicit method. The resulting constrained regularized optimization problem is minimized iteratively by employing a MATLAB toolbox subroutine.