The order of convergence in the stefan problem with vanishing specific heat

The paper is concerned with the two-phase Stefan problem with a small parameter ε, which coresponds to the specific heat of the material. It is assumed that the initial condition does not coincide with the solution for t = 0 of the limit problem related to ε = 0. To remove this discrepancy, an auxiliary boundary layer type function is introduced. It is proved that the solution to the two-phase Stefan problem with parameter ε differs from the sum of the solution to the limit Hele-Shaw problem and a boundary layer type function by quantities of order O(ε). The estimates are obtained in Hölder norms. Bibliography: 13 titles. © 2011 Springer Science+Business Media, Inc.