# Irina Kogan : Geometry of Hyperbolic Conservation Laws

We consider the problem of constructing systems of hyperbolic conservation laws in one space dimension with prescribed geometry in state space: the eigenvectors of the Jacobian of the flux are given. This is formulated as a system of algebraic-differential equations whose solution space is analyzed using Darboux and Cartan-K\"ahler theorems. It turns out that already the case with three equations is fairly complex. We give a complete list of possible scenarios for the general systems of two and three equations and for rich systems (i.e. when the given eigenvector fields are pairwise in involution) of arbitrary size. As an application we characterize conservative systems with the same eigencurves as compressible gas dynamics.

This is joint work with Kris Jenssen (Penn State University)

**Category**: Geometry and Topology**Duration**: 01:34:47**Date**: March 31, 2009 at 4:25 PM**Views**: 118-
**Tags:**seminar, Geometry/topology Seminar

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