Solvability of an axisymmetric problem for a nonlinear parabolic equation in domains with a non-cylindrical or unknown boundary. II

The regular solvability of a Stefan-type problem for a quasi-linear three-dimensional parabolic equation with axial symmetry is proved, and, in general, in time. The equation describes the processes of phase transitions of a substance from one state to another. The boundary of the transition phase is unknown, is determined together with the solution and belongs to the class $W^1_2$. Unlike the well-known Stefan problem, when the latent heat of melting of a substance is known, here we consider the problem when it is necessary to determine this characteristic if the volume of the melted substance for a given period is known.