Geodesic
The Riemann problem in gasdynamics
Electronic Journal of Differential Equations, Tome 2009 (2009).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this note we give a proof of the existence of a solution to the Riemann problem in one-dimensional gasdynamics. Lax's 1957 paper on conservation laws leaves no doubt that such a solution exists, but it seems to us that there may be interest in a brief and explicit proof favorable to numerical computations. Our procedure also allows us to give a simple characterization of those problems in which a given wave is a shock or a rarefaction wave. In the final section we prove a result of Von Neumann's concerning the overtaking of two shocks. This paper was written in 1969 and is being published now at the suggestion of Jerry Goldstein, whose editorial note is included.
Classification : 35L03, 35L65, 35L67, 76L05
Keywords: Riemann problem, shock wave, rarefaction wave 
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Conway, Edward Daire; Rosencrans, Steven I. The Riemann problem in gasdynamics. Electronic Journal of Differential Equations, Tome 2009 (2009). http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a31/