title: Riemann problems with non--local point constraints and capacity drop.
abstract: 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 [Andreianov, Donadello, Rosini, Crowd dynamics and conservation laws with nonlocal 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.
authors: Laboratoire de Mathematiques CNRS UMR 6623, Universite de Franche-Comte, 16 route de Gray, 25030 Besançon Cedex, France. boris.andreianov@univ-fcomte.fr.
authors: Boris
authors: B
authors: Andreianov
authors: Carlotta
authors: C
authors: Donadello
authors: Ulrich
authors: U
authors: Razafison
authors: Massimiliano D
authors: MD
authors: Rosini
mesh_terms: D000465:Algorithms; D002462:Cell Membrane / Q000378:metabolism; D003198:Computer Simulation; D019277:Entropy; D006801:Humans; D008954:Models, Biological; D008962:Models, Theoretical; D011336:Probability; D014186:Transportation