Optimization of partial differential equations for minimizing the roughness of laser cutting surfaces

This work introduces a mathematical model for laser cutting which involves two coupled nonlinear partial differential equations. The model will be investigated by linear stability analysis to study the occurence of ripple formations at a cutting surface. We define a measurement for the roughness of the cutting surface and give a method for minimizing the roughness with respect to process parameters. A numerical solution of this nonlinear optimization problem will be presented and compared with the results of the linear stability analysis.