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 | References | Similar Articles | Additional Information

Abstract: This paper contains a proof of the existence of solutions to the Riemann problem for a class of 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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Additional Information

**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.