Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 123, pp. 1-7.
Title: The Riemann problem in gasdynamics
Authors: Edward Daire Conway (Tulane Univ., New Orleans, LA, USA)
Steven I. Rosencrans (Tulane Univ., New Orleans, LA, USA)
Abstract:
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.
Submitted August 2, 2009. Published September 29, 2009.
Math Subject Classifications: 35L03, 35L65, 35L67, 76L05.
Key Words: Riemann problem; shock wave; rarefaction wave.