2024/11/19 by Felisia Angela Chiarello, Chiarello, Felisia Angela, Simone Fagioli +3
Engineering · Mathematics · #35B40 #35L45 #35Q70 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #Primary: 35L65 #Secondary: 35D30
paper · pdf · doi:10.48550/arxiv.2411.12531
openalex publication_date 2024/11/19 · openalex created_date 2024/11/21 · openalex updated_date 2026/08/01
This paper is concerned with one-dimensional 2 x 2 systems of conservation laws with a flux f=f(x, U) that is discontinuous with respect to the spatial variable. No monotonicity assumption is imposed on the mapping x → f(x,U). We introduce a Kruzhkov-type entropy condition and establish the global existence of entropy solutions for large data. The proof relies on a wave-front tracking approximation. The main technical novelty consists in the introduction of adapted Riemann invariant coordinates, specifically designed to account for the discontinuities of the flux, which yield a uniform-in-time bound on the total variation of the approximate solutions Un(t). We also outline several alternative approaches that may lead to existence results under possibly weaker assumptions. As an application, we propose second-order vehicular traffic models on inhomogeneous roads featuring abrupt ''collective'' changes in the speed law or road capacity.