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A free boundary problem arising from the process of Czochralski crystal growth. (English) Zbl 1301.35222

Summary: A free boundary problem from the process of Czochralski crystal growth is studied. Existence and uniqueness of the solution are established in the cases when the melt is superheated (\(\delta > 1\)) and the melt is not superheated (\(\delta > 1\)) respectively. The behavior of the free boundary is discussed. The growth rate is bounded in either case and the maximum growth rate can be estimated in terms of given parameters.

MSC:

35R35 Free boundary problems for PDEs
80A22 Stefan problems, phase changes, etc.
74N05 Crystals in solids
74N20 Dynamics of phase boundaries in solids
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