Codimension-one Riemann solutions: Missing rarefactions in transitional wave groups (Q5954447)

This interesting paper is devoted to the investigation of the existence of Riemann solutions of systems of two conservation laws in one spatial dimension, \(U_t+F(U)_x=0\), \(t>0\), \(x\in \mathbb R\), \(U(x,t)\in \mathbb R^2\), and \(F:\mathbb R^2\to\mathbb R^2\) is a smooth map. The initial data are piecewise constant with single jump at \(x=0\), and then the considered problem is known as the Riemann problem. Three degeneracies that can occur only in transitional wave groups, together with the degeneracies that pair with them are studied in detail. Conditions for a codimension-one degeneracy are identified in each case. Conditions for folding of the Riemann solution surface are investigated as well.