The numerical solution of the inverse Stefan problem in two space variables
Abstract
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 initialboundary data subject to regularizing constraints (thus making the problem wellposed in the sense that the solution now depends continuously on the data). Two numerical examples are given which make use of a linear semiinfinite programming method recently developed by Hettich and Zencke.
 Publication:

SIAM Journal of Applied Mathematics
 Pub Date:
 October 1984
 Bibcode:
 1984SJAM...44..996C
 Keywords:

 Boundary Value Problems;
 Free Boundaries;
 Melting;
 Solids;
 StefanBoltzmann Law;
 Thermodynamics;
 Cartesian Coordinates;
 Cauchy Problem;
 Linear Programming;
 Polar Coordinates;
 Fluid Mechanics and Heat Transfer