Extend sequential transversality beyond strictly hyperbolic genuinely nonlinear systems

Extend the sequential-transversality framework to hyperbolic conservation-law regimes that violate genuine nonlinearity or strict hyperbolicity, including composite waves, contact discontinuities, coinciding or crossing characteristic speeds, and the corresponding adapted admissibility criteria.

Background

The paper’s main structural-stability and genericity results assume strict hyperbolicity and genuine nonlinearity, thereby restricting the analysis to classical Lax shocks and rarefactions. The authors explicitly identify extension to non-convex systems with composite waves and to systems with coinciding or crossing characteristic speeds as an unresolved direction. Such an extension would require replacing the present Lax-wave formulation with admissibility criteria appropriate to the additional wave types.