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Stefan problems in non-cylindrical domains arising in Czochralski process of crystal growth

Fukao T., Kenmochi N., Pawłow I.

Control and Cybernetics

2003

Vol. 32, no 2

201-221

In this paper we discuss a two-phase Stefan problem with convection in a non-cylindrical (time-dependent) domain. This work is motivated by phase change phenomenon arising in the Czochralski process of crystal growth. The time-dependence of domain is a mathematical description of the situation in which the material domain changes its shape with time by crystal growth. We consider the so-called enthalpy formulation for it and give its solvability, assuming that the time-dependence of the material domain is prescribed and smooth enough in time, and the convective vector is prescribed, too. Our main idea is to apply the theory of quasi-linear equations of parabolic type.