The unique limit of the Glimm scheme

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We introduce the definitions of a standard Riemann semigroup and of a viscosity solution for a nonlinear hyperbolic system of conservation laws. For a class including general 2×2 systems, it is proved that the solutions obtained by a wavefront tracking algorithm or by the Glimm scheme are precisely the semigroup trajectories. In particular, these solutions are unique and depend Lipschitz continuously on the initial data in the L1 norm.

Original languageEnglish (US)
Pages (from-to)205-230
Number of pages26
JournalArchive for Rational Mechanics and Analysis
Issue number3
StatePublished - Sep 1 1995

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering


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