2014/03/17 by Boris Andreianov, Boris Andreïanov, Carlotta Donadello +6
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Traffic control and management #math.AP
paper · pdf · doi:10.48550/arxiv.1403.4203
19 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1304.6282
arxiv created 2014/03/17 · openalex publication_date 2014/03/17 · arxiv updated 2014/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the present note we discuss in details the Riemann problem for a one--dimensional hyperbolic conservation law subject to a point constraint. We investigate how the regularity of the constraint operator impacts the well--posedness of the problem, namely in the case, relevant for numerical applications, of a discretized exit capacity. We devote particular attention to the case in which the constraint is given by a non--local operator depending on the solution itself. We provide several explicit examples. We also give the detailed proof of some results announced in the paper [Andreainov, Donadello, Rosini, "Crowd dynamics and conservation laws with non--local point constraints and capacity drop", which is devoted to existence and stability for a more general class of Cauchy problems subject to Lipschitz continuous non--local point constraints.