Industrial Mathematics Institute, Johannes Kepler University,

69 Altenbergerstrasse, A-4040 Linz, AUSTRIA

E-mail: bila@indmath.uni-linz.ac.at

**Application of symmetry analysis to a PDE arising in
the car windscreen design**

**Abstract:**

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".*