The unique limit of the Glimm scheme

Research output: Contribution to journalArticle

81 Citations (Scopus)

Abstract

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
Volume130
Issue number3
DOIs
StatePublished - Sep 1 1995

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Glimm Scheme
Semigroup
Nonlinear Hyperbolic Systems
Hyperbolic Systems of Conservation Laws
L1-norm
Particular Solution
Viscosity Solutions
Wave Front
Lipschitz
Trajectory
Wavefronts
Conservation
Trajectories
Viscosity

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

Cite this

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The unique limit of the Glimm scheme. / Bressan, Alberto.

In: Archive for Rational Mechanics and Analysis, Vol. 130, No. 3, 01.09.1995, p. 205-230.

Research output: Contribution to journalArticle

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