Geodesic
Recovering the timewise reaction coefficient for a two-dimensional free boundary problem
Eurasian journal of mathematical and computer applications, Tome 7 (2019) no. 4, pp. 66-85.

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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.
Keywords: Inverse coefficient identification problem, Free boundary, Two-dimensional parabolic equation, Tikhonov regularization, Nonlinear optimization. 
@article{EJMCA_2019_7_4_a4,
     author = {M. J. Huntul},
     title = {Recovering the timewise reaction coefficient for a two-dimensional free boundary problem},
     journal = {Eurasian journal of mathematical and computer applications},
     pages = {66--85},
     publisher = {mathdoc},
     volume = {7},
     number = {4},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJMCA_2019_7_4_a4/}
}
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M. J. Huntul. Recovering the timewise reaction coefficient for a two-dimensional free boundary problem. Eurasian journal of mathematical and computer applications, Tome 7 (2019) no. 4, pp. 66-85. http://geodesic.mathdoc.fr/item/EJMCA_2019_7_4_a4/