Papers › Generic Structural Stability for 2 ×2 Systems of Hyperbolic Conservation Laws
Generic Structural Stability for 2 ×2 Systems of Hyperbolic Conservation Laws
Hong Kiat Tan, Andrea L. Bertozzi
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
This paper presents a proof of generic structural stability for Riemann solutions to 2 ×2 system of hyperbolic conservation laws in one spatial variable, without diffusive terms. This means that for almost every left and right state, shocks and rarefaction solutions of the same type are preserved via perturbations of the flux functions, the left state, and the right state. The main assumptions for this proof involve standard assumptions on strict hyperbolicity and genuine non-linearity, a technical assumption on directionality of rarefaction curves, and the regular manifold (submersion) assumption motivated by concepts in differential topology. We show that the structural stability of the Riemann solutions is related to the transversality of the Hugoniot loci and rarefaction curves in the state space. The regular manifold assumption is required to invoke a variant of a theorem from differential topology, Thom's parametric transversality theorem, to show the genericity of transversality of these curves. This in turn implies the genericity of structural stability. We then apply this theorem to two examples: the p-system and a 2 ×2 system governing the evolution of gravity-driven monodisperse particle-laden thin films. In particular, we illustrate how one can verify all the above assumptions for the former, and apply the theorem to different numerical and physical aspects of the system governing the latter.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections