The unique limit of the Glimm scheme

Alberto Bressan

doi:10.1007/BF00392027

The unique limit of the Glimm scheme

Alberto Bressan

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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 language	English (US)
Pages (from-to)	205-230
Number of pages	26
Journal	Archive for Rational Mechanics and Analysis
Volume	130
Issue number	3
DOIs	https://doi.org/10.1007/BF00392027
State	Published - Sep 1 1995

All Science Journal Classification (ASJC) codes

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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10.1007/BF00392027

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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.",

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AB - 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.

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The unique limit of the Glimm scheme

Abstract

All Science Journal Classification (ASJC) codes

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