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Abstract
It was shown in [1, 2, 4], when approximating the parabolic Stefan problem by a family of optimalcontrol problems in which the controlling parameter is the form of the region in which the state-temperature function of the liquid phase is defined, that the classical solution of the Stefan problem is the limit of the solutions of the corresponding approximation problems in the metrics of approximate functional spaces. The structure of the optimal-control approximation problems which model the Stefan problem is investigated, the necessary conditions for these problems to be solvable are obtained, and a proof of the convergence of the proposed approximate methods of solving them is given.
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