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Existence of Relaxation Shock Profiles for Hyperbolic Conservation Laws

Wen-An Yong and Kevin Zumbrun
SIAM Journal on Applied Mathematics
Vol. 60, No. 5 (May, 2000), pp. 1565-1575
Stable URL: http://www.jstor.org/stable/3061701
Page Count: 11
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Existence of Relaxation Shock Profiles for Hyperbolic Conservation Laws
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Abstract

In this paper we prove that, like viscosity, relaxation can also smooth weak shocks for strict hyperbolic conservation laws as equilibium systems of hyperbolic relaxation systems under some natural structural conditions. These conditions were derived previously by Yong from stability considerations and hence are entirely analogous to the Majda-Pego criterion of the viscous case. The proof involves a new parametrization of Hugoniot curves and a delicate analysis of the algebraic structure of relaxation systems as well as construction of an appropriate center manifold.

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