Mathematical modelling and stability analysis for laser cutting

Mathematical modelling and stability analysis for the thermal separation process of laser cutting will be considered. The process can be modelled as a free boundary problem of non-linear 2D partial differential equations with two moving boundaries describing the dynamical behaviour of the arising melt flow. An approximate reduced 1D model will be derived by asymptotic expansion methods. This model allows for linear stability analysis of the system, which will be applied for different levels of approximation qualities. The results are illustrated by numerical simulation of the free boundary and the reduced problem.