One Dimensional Hyperbolic Conservation Laws: Past and Future

2023/10/25 by Alberto Bressan, Bressan, Alberto · 1 citation
Engineering · Mathematics · #35L45 #35L65 #35L67 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2310.16707

openalex publication_date 2023/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Aim of these notes is provide a brief review of the current well-posedness theory for hyperbolic systems of conservation laws in one space dimension, also pointing out open problems and possible research directions. They supplement the slides of the short course given by the author in Erice, May 2023, available at: sites.google.com/view/erice23/speakers-and-slides.

Cited by

• Quantitative weak-BV stability of "wild'' solutions to compressible Euler equations, with a view towards higher systems

Related

• Hyperbolic systems of conservation laws in one space dimension
• Well-posedness theory for geometry compatible hyperbolic conservation laws on manifolds
• An Overview on Some Results Concerning the Transport Equation and its Applications to Conservation Laws
• An Ill Posed Cauchy Problem for a Hyperbolic System in Two Space Dimensions
• Systems of conservation laws in higher space dimensions