Two-phase Stefan problem with vanishing specific heat

We prove the unique solvability of the two-phase Stefan problem with a small parameter $\varepsilon\in[0;\varepsilon_0]$ at the time derivative in the heat equations. The solution is obtained on a certain time interval $[0;t_0]$ independent of $\varepsilon$. We compare the solution of the Stefan problem with the solution to the Hele–Shaw problem corresponding to the case $\varepsilon=0$. We do not assume that the solutions of both problems coincide at the initial moment of time. Bibl. – 18 titles.