Persistence of generalized roll-waves under viscous perturbation

2010/04/20 by Valérie Blanc, Valérie Le Blanc, Blanc, Valérie Le
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Quantum chaos and dynamical systems #advanced mathematical theories #math.AP

paper · pdf · doi:10.48550/arxiv.1004.3459

arxiv created 2010/04/20 · openalex publication_date 2010/04/20 · arxiv updated 2010/05/02 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

The purpose of this article is to study the persistence of solution of a hyperbolic system under small viscous perturbation. Here, the solution of the hyperbolic system is supposed to be periodic: it is a periodic perturbation of a roll-wave. So, it has an infinity of shocks. The proof of the persistence is based on an expansion of the viscous solution and estimates on Green's functions.

Related

• Note on the stability of viscous roll-waves
• Nonlinear stability of viscous roll waves
• Linear damping estimates for periodic roll wave solutions of the inviscid Saint-Venant equations and related systems of hyperbolic balance laws
• Stability of strong viscous shock wave under periodic perturbation for 1-D isentropic Navier-Stokes system in the half space
• Perturbation theory of the compressible Navier-Stokes equations and its application