Existence of solutions to the Riemann problem for a class of hyperbolic conservation laws exhibiting a parabolic degeneracy

Ohwa, Hiroki

doi:10.1090/S0033-569X-2012-01254-5

Author: Hiroki Ohwa
Journal: Quart. Appl. Math. 70 (2012), 345-356
MSC (2010): Primary 35L45, 35L65
DOI: https://doi.org/10.1090/S0033-569X-2012-01254-5
Published electronically: February 29, 2012
MathSciNet review: 2953107
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Abstract: This paper contains a proof of the existence of solutions to the Riemann problem for a class of $2\times 2$ hyperbolic conservation laws exhibiting a parabolic degeneracy. The method used in this paper is based upon the vanishing viscosity approach. This approach enables us to establish the existence of solutions to the Riemann problem for those systems which do not satisfy the genuine nonlinearity condition and the shock admissibility condition.

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