Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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


Author: Hiroki Ohwa
Journal: Quart. Appl. Math. 70 (2012), 345-356
MSC (2010): Primary 35L45, 35L65
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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Hiroki Ohwa
Affiliation: Graduate School of Education, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku-ku, Tokyo, 169-8050, Japan
Email: ohwa-hiroki@suou.waseda.jp

DOI: https://doi.org/10.1090/S0033-569X-2012-01254-5
Keywords: Conservation laws, nonlinear wave equation, the Riemann problem, the vanishing viscosity approach
Received by editor(s): October 4, 2010
Published electronically: February 29, 2012
Article copyright: © Copyright 2012 Brown University
The copyright for this article reverts to public domain 28 years after publication.


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