2021/03/24 by Felisia Angela Chiarello, Chiarello, Felisia Angela, Contreras, Harold Deivi +1
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Traffic control and management
paper · pdf · doi:10.48550/arxiv.2103.13362
openalex publication_date 2021/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a 1D scalar conservation law whose non-local flux has a single spatial discontinuity. This model is intended to describe traffic flow on a road with rough conditions. We approximate the problem through an upwind-type numerical scheme and provide compactness estimates for the sequence of approximate solutions. Then, we prove the existence and the uniqueness of entropy weak solutions. Numerical simulations corroborate the theoretical results and the limit model as the kernel support tends to zero is numerically investigated.