Loss of hyperbolicity changes the number of wave groups in Riemann problems

Abstract

Themain goal of ourwork is to showthat there exists a class of 2x2 Riemann problems for which the solution comprises a singlewave group for an open set of initial conditions. This wave group comprises a 1-rarefaction joined to a 2-rarefaction, not by an intermediate state, but by a doubly characteristic shock, 1-left and 2-right characteristic. In order to ensure that perturbations of initial conditions do not destroy the adjacency of the waves, local transversality between a composite curve foliation and a rarefaction curve foliation is necessary.