Representation of weak limits and definition of nonconservative products

Philippe G. LeFloch*, Athanasios Tzavaras

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

78 Scopus citations


The goal of this article is to show that the notion of generalized graphs is able to represent the limit points of the sequence {g(un) dun} in the weak-(black star sing) topology of measures when {un} is a sequence of continuous functions of uniformly bounded variation. The representation theorem induces a natural definition for the nonconservative product g(u) du in a BV context. Several existing definitions of nonconservative products are then compared, and the theory is applied to provide a notion of solutions and an existence theory to the Riemann problem for quasi-linear, strictly hyperbolic systems.

Original languageEnglish (US)
Pages (from-to)1309-1342
Number of pages34
JournalSIAM Journal on Mathematical Analysis
Issue number6
StatePublished - Jan 1 1999


  • Hyperbolic systems
  • Nonconservative products
  • Self-similar solution
  • Shock wave

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics


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