Mathematical analysis of the pulling method for crystal growth. 

The pulling method due to Czochralski is well-known as a practical 
way for the production of single crystals from mert substances. But 
the theoretical analysis of its mathematical model seems still incomplete. 
In this talk we propose a more realistic mathematical model for the pulling 
method and discuss the solvability. Our model is a system of nonlinear 
parabolic equations formulated in a time-dependent domain.