Acta Applicandae Mathematica

, Volume 88, Issue 3, pp 269–329

The Geometry of 2 × 2 Systems of Conservation Laws


DOI: 10.1007/s10440-005-9002-5

Cite this article as:
Basto-Gonçalves, J. & Reis, H. Acta Appl Math (2005) 88: 269. doi:10.1007/s10440-005-9002-5


We consider one typical two-parameter family of quadratic systems of 2 × 2 conservation laws, and study the geometry of the behaviour of the possible solutions of the Riemann problem near an umbilic point, following the geometric approach presented by Isaacson, Marchesin, Palmeira, Plohr, in A global formalism for nonlinear waves in conservation laws, Commun. Math. Phys. (1992). The corresponding phase portraits for the rarefaction curves, shock curves and composite curves are discussed.

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Centro de Matemática da Universidade do PortoPortoPortugal