An axisymmetric transient model for the forward problem of the
sublimation growth of SiC bulk single crystals is presented. The model for
the gas phase consists of balance equations for energy, mass, and momentum,
including reaction-diffusion equations. In solid components, the model
consists of nonlinear heat transport equations including nonlocal coupling
via integral operators due to radiation. Induction heating is modeled by
an axisymmetric complex-valued magnetic scalar potential that is determined
as the solution of an elliptic problem.
The optimization goals of the applied problem are translated into a
mathematical control problem. The main control parameters are the heating
power and the position of the induction coil.
Both the stationary and the transient heat problem are solved numerically,
and first numerical results for the control of the heat transport problem
are discussed.
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