Transmission-Stefan Problems Arising in Czochralski Process of Crystal Growth
T. Fukao, Nobuyuki Kenmochi, Irena Pawłow · Birkhäuser Basel eBooks · 2003
We consider a transmission problem of two parabolic partial differential equations as a mathematical model of the Czochralski crystal growth process. Originally this process is a three-phase system and involves the three interfaces of solid-liquid, liquid-gas, and solid-gas, which should be determined as a part of solution from the mathematical point of view. Nevertheless, assuming that the solid-gas and liquid-gas interfaces are prescribed, we propose in this paper a transmission problem composed of a linear heat equation in the gas region and a nonlinear degenerate parabolic equation in the material region as a simplified mathematical model of the Czochralski process. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.