Archive for Rational Mechanics and Analysis

, Volume 130, Issue 3, pp 205–230

The unique limit of the Glimm scheme

  • Alberto Bressan

DOI: 10.1007/BF00392027

Cite this article as:
Bressan, A. Arch. Rational Mech. Anal. (1995) 130: 205. doi:10.1007/BF00392027


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.

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Alberto Bressan
    • 1
  1. 1.S.I.S.S.A.TriesteItaly