Abstract
We consider the Riemann problem for a system of two conservation laws of mixed type. We show by constructing two distinct solutions for a non trivial class of Riemann problem data that the viscous profile entropy condition is insufficient to guarantee uniqueness of the solution. This model possesses transitional shocks — or saddle to saddle connections of the associated dynamical system — of a kind not yet observed in conservation laws with quadratic polynomial flux functions.
This research was supported in Brazil by CNPq, FAPERJ and in the U.S.A. by IMA with funds provided by NSF
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Azevedo, A.V., Marchesin, D. (1990). Multiple Viscous Profile Riemann Solutions in Mixed Elliptic-Hyperbolic Models for Flow in Porous Media. In: Keyfitz, B.L., Shearer, M. (eds) Nonlinear Evolution Equations That Change Type. The IMA Volumes in Mathematics and Its Applications, vol 27. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9049-7_1
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