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The unique limit of the Glimm scheme

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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 L 1 norm.

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  1. S.I.S.S.A., Via Beirut 4, 34014, Trieste, Italy

    Alberto Bressan

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  1. Alberto Bressan
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Communicated by C. Dafermos

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Bressan, A. The unique limit of the Glimm scheme. Arch. Rational Mech. Anal. 130, 205–230 (1995). https://doi.org/10.1007/BF00392027

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