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VOL. 47.1 | 2007 Survey of admissible shock waves for $2 \times 2$ systems of conservation laws with an umbilic point
Fumioki Asakura, Mitsuru Yamazaki

Editor(s) Hideo Kozono, Takayoshi Ogawa, Kazunaga Tanaka, Yoshio Tsutsumi, Eiji Yanagida

Abstract

In this survey note, we consider $2 \times 2$ systems of conservation laws with an umbilic point. At the umbilic point, the characteristic speeds coincide and the Jacobian matrix of the flux functions is diagonalizable. It is shown that if there are no undercompressive shocks with viscous shock profile then any compressive shock has a viscous shock profile and any overcompressive shock has a infinitely many viscous shock profiles.

Information

Published: 1 January 2007
First available in Project Euclid: 16 December 2018

zbMATH: 1145.35084
MathSciNet: MR2387227

Digital Object Identifier: 10.2969/aspm/04710087

Rights: Copyright © 2007 Mathematical Society of Japan

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