Application of symmetry analysis to a PDE arising in the car windscreen design
A new approach to parameter identification problems related to the theory of inverse problems by using the symmetry group theory. In particular, one studies the second order partial differential equation for the Young's modulus that arises in the design of car windscreens by gravity sag bending process. Exploiting the invariance of this differential equation under certain symmetry subgroups, one can give a natural connection between classes of parameter (data) functions (which are the car windscreen shapes) and the Young's modulus (that can be linked to the temperature) in terms of the associated invariants.
This work is supported by the Austrian Science Foundation FWF, Project SFB 1308 ``Large Scale Inverse Problems".