Istituto di Matematica Applicata e Tecnologie Informatiche     
Fukao T., Kenmochi N., Pawlow I. Mathematical Modeling for Czochralski Process. Preprint ercim.cnr.ian//2002-1279, 2002.
We consider a transmission problem of two parabolic partial differential equations as a mathematical model of 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, in this paper, assuming that the solid-gas and liquid-gas interfaces are prescribed, we propose 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.
Subject 82B26,80A22

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