Systems of hyperbolic conservation laws with prescribed eigencurves

Helge Kristian Jenssen, Irina A. Kogan

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We study the problem of constructing systems of hyperbolic conservation laws in one space dimension with prescribed eigencurves, i.e. the eigenvector fields of the Jacobian of the flux are given. We formulate this as a typically overdetermined system of equations for the eigenvalues-to-be. Equivalent formulations in terms of differential and algebraic-differential equations are considered. The resulting equations are then analyzed using appropriate integrability theorems (Frobenius, Darboux and CartanKähler). We give a complete analysis of the possible scenarios, including examples, for systems of three equations. As an application we characterize conservative systems with the same eigencurves as the Euler system for 1-dimensional compressible gas dynamics. The case of general rich systems of any size (i.e. when the given eigenvector fields are pairwise in involution; this includes all systems of two equations) is completely resolved and we consider various examples in this class.

Original languageEnglish (US)
Pages (from-to)211-254
Number of pages44
JournalJournal of Hyperbolic Differential Equations
Volume7
Issue number2
DOIs
StatePublished - Jun 2010

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics(all)

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