In the steady-state equilibrium, the cutting front arises in such a way that the locally absorbed power density corresponds to the local heat-flow requirement. Beside the power balance, mass and force balance have to be fulfilled simultaneously.

The above mentioned power, mass and force balances and a boundary layer approximation of the heat flow at the flank as well as two continuity conditions for vertex and flank provide the governing equations to be solved for the calculation of each segment.