Codimension-One Riemann Solutions: Classical Missing Rarefaction Cases

AbstractThis paper is the third in a series that undertakes a systematic investigation of Riemann solutions of systems of two conservation laws in one spatial dimension. Sixty-three codimension-one degeneracies of such solutions have been identified at which strict hyperbolicity is maintained. In this paper, 18 of the degeneracies (9 pairs), constituting the most classical degeneracies, are studied in detail. Precise conditions for a codimension-one degeneracy are identified in each case, as are conditions for folding of the Riemann solution surface, which can occur in 4 of the cases. Such folding gives rise to local multiplicity or nonexistence of Riemann solutions