Establish regularity of composite wave curves at sonic attachment points

Establish the regularity of composite wave curves at their sonic attachment points in non-convex systems with alternating rarefaction fans and sonic shocks, so that the enlarged sequential-transversality framework can be rigorously applied to fixed composite-wave patterns.

Background

The authors explain that, after relaxing genuine nonlinearity, wave curves may be constructed using alternating fans and sonic shocks, with attachment equations and Liu’s E-condition replacing the classical Lax formulation. They identify the regularity of the resulting composite wave curves at attachment points as the specific technical obstacle preventing completion of this extension.