Application of Symmetry Analysis to a PDE Arising in the Car Windscreen Design
Abstract
Our aim is to find the symmetry reductions related to the PDE (8) hidden by the nonlinearity that occurs between the data and the parameter -> group of transformations that leave the equation unchanged, which also relate the inverse and the direct problem -> knowledge of the invariants of these group actions allows us to write the target shape and the parameter in terms of them, and therefore, to reduce the order of the studied model -> we find again the obvious result that a Young's modulus constant corresponds to a data which is a solution of an non- homogeneous biharmonic equation -> the circular case considered by Salazar and Westbrook is a particular case of our study -> other target shapes which are not radial functions can be considered -> the equation (8) is invariant under scaling transformations -> target shapes modelled by homogeneous functions can be analyzed as well. -> in particular, we are interested in target shapes modelled by homogeneous polynomials defined on elliptical domains or square domains with rounded corners.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 03, 2005
- Accession Number
- ADA433612
Entities
People
- Heinz W. Engl
- Nicoleta Bila
- Peter Olver
- Phillip Kugler
Organizations
- Johannes Kepler University Linz