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