Riemann problems with non--local point constraints and capacity drop
  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. 
Boris Andreianov (LM-Besan\c{c}on), Carlotta Donadello   (LM-Besan\c{c}on), Ulrich Razafison (LM-Besan\c{c}on), Massimiliano...
math.AP