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

Weishi Liu

doi:10.3934/dcds.2004.10.871

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2004, Volume 10, Issue 4: 871-884. Doi: 10.3934/dcds.2004.10.871

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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: October 31, 2002

Revised: November 30, 2003

Published: September 2004

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Abstract

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.

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Mathematics Subject Classification: 35L65, 35L67, 37D15, 37G25.

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