, Volume 130, Issue 3, pp 205-230

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.

Communicated by C. Dafermos