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October  2004, 10(4): 871-884. doi: 10.3934/dcds.2004.10.871

Multiple viscous wave fan profiles for Riemann solutions of hyperbolic systems of conservation laws

Weishi Liu 1,

1. 

Department of Mathematics, University of Kansas, Lawrence, KS 66045

Received  November 2002 Revised  December 2003 Published  March 2004

For a system of hyperbolic conservation laws in one space dimension, we study the viscous wave fan admissibility of Riemann solutions. In particular, we show that structurally unstable Riemann solutions with compressive and overcompressive viscous shocks, and with constant portions crossing the hypersurfaces of eigenvalues admit viscous wave fan profiles. The main tool used in the study is the center manifold theorem for invariant sets and the exchange lemmas for singular perturbation problems.
Keywords: viscous wave fan profiles, singular perturbations, exchange lemmas., Riemann solutions, Hyperbolic conservation laws.
Mathematics Subject Classification: 35L65, 35L67, 37D15, 37G2.
Citation: Weishi Liu. Multiple viscous wave fan profiles for Riemann solutions of hyperbolic systems of conservation laws. Discrete & Continuous Dynamical Systems - A, 2004, 10 (4) : 871-884. doi: 10.3934/dcds.2004.10.871
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