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

The paper is concerned with a two-phase Stefan problem with a small parameter $\varepsilon$ which coresponds to the specific heat of the material. We assume that the initial condition does not coincide with the value at $t=0$ of the solution to the limit problem related to $\varepsilon=0$. To remove this discrepancy, we introduce an auxiliary boundary layer type function. We prove that the solution to the two-phase Stefan problem with parameter $\varepsilon$ differs from the sum of the solution to the limit Hele–Shaw problem and the boundary layer type function by quantities of the order $O(\varepsilon)$. The estimates are obtained in Hölder norms. Bibl. 13 titles.