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APPROXIMATE SHOCK CURVES FOR NON-CONSERVATIVE HYPERBOLIC SYSTEMS IN ONE SPACE DIMENSION

Laboratoire de Mathématique, Université d'Orsay 91405 Orsay Cedex, France

Centre de Mathématiques et de Leurs Applications, Ecole Normale Supérieure de Cachan, 61 Avenue du, Président Wilson 94235 Cachan Cedex, France

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and

BENOIT MERLET

Laboratoire de Mathématique, Université d'Orsay 91405 Orsay Cedex, France

Centre de Mathématiques et de Leurs Applications, Ecole Normale Supérieure de Cachan, 61 Avenue du, Président Wilson 94235 Cachan Cedex, France

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https://doi.org/10.1142/S0219891604000251Cited by:12 (Source: Crossref)

Abstract

For non-conservative hyperbolic systems several definitions of shock waves have been introduced in the literature. In this paper, we propose a new and simple definition in the case of genuinely nonlinear fields. Relying on a vanishing viscosity process we prove the existence of shock curves for viscosity matrix commuting with the matrix of the hyperbolic system. This setting generalizes a recent result by Bianchini and Bressan. Furthermore we prove that all definitions agree to third order near a given state.

Keywords:

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