On one proof of the classical solvability of the Hele-Shaw problem with free boundary

We consider the Stefan problem for a parabolic equation with a small parameter as the coefficient of the derivative with respect to time. We justify the limit transition as the small parameter tends to zero, which enables us to prove the classical solvability of the Hele-Shaw problem with free boundary in the small with respect to time. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50; No. 11, pp. 1452–1462, November, 1998.