Geodesic
Two-phase Stefan problem with vanishing specific heat
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 39, Tome 362 (2008), pp. 337-363

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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. 
@article{ZNSL_2008_362_a12,
     author = {E. V. Frolova},
     title = {Two-phase {Stefan} problem with vanishing specific heat},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {337--363},
     publisher = {mathdoc},
     volume = {362},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_362_a12/}
}
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E. V. Frolova. Two-phase Stefan problem with vanishing specific heat. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 39, Tome 362 (2008), pp. 337-363. http://geodesic.mathdoc.fr/item/ZNSL_2008_362_a12/