Geodesic
Solvability of an axisymmetric problem for a nonlinear parabolic equation in domains with a non-cylindrical or unknown boundary. II
Čelâbinskij fiziko-matematičeskij žurnal, Tome 7 (2022) no. 1, pp. 43-53

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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.
Keywords: Stefan's condition, quasilinear parabolic equation, non-cylindrical domain, compactness theorem. 
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     author = {A. G. Podgaev},
     title = {Solvability of an axisymmetric problem for a nonlinear parabolic equation in domains with a non-cylindrical or unknown boundary. {II}},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {43--53},
     publisher = {mathdoc},
     volume = {7},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2022_7_1_a4/}
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A. G. Podgaev. Solvability of an axisymmetric problem for a nonlinear parabolic equation in domains with a non-cylindrical or unknown boundary. II. Čelâbinskij fiziko-matematičeskij žurnal, Tome 7 (2022) no. 1, pp. 43-53. http://geodesic.mathdoc.fr/item/CHFMJ_2022_7_1_a4/