The numerical solution of the inverse Stefan problem in two space variables

A method is given for solving the inverse Stefan problem for the heat equation in two space variables. The approach is based on using a complete family of solutions to the heat equation (thus reducing the dimensionality of the problem by one) and minimizing the maximal defect in the initial-boundary data subject to regularizing constraints (thus making the problem well-posed in the sense that the solution now depends continuously on the data). Two numerical examples are given which make use of a linear semi-infinite programming method recently developed by Hettich and Zencke.