Geodesic
On conditions for the existence of a classical solution of the modified Stefan problem (the Gibbs–Thomson law)
Sbornik. Mathematics, Tome 75 (1993) no. 1, pp. 221-246 Cet article a éte moissonné depuis la source Math-Net.Ru

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Sufficient conditions close to necessary are obtained for the existence of a solution (unique for $\sigma>0$ and $\beta>0$) of a solution of the modified Stefan problem on a small time interval. 
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E. V. Radkevich. On conditions for the existence of a classical solution of the modified Stefan problem (the Gibbs–Thomson law). Sbornik. Mathematics, Tome 75 (1993) no. 1, pp. 221-246. http://geodesic.mathdoc.fr/item/SM_1993_75_1_a12/

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