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.

Riemann problems with non-local point constraints and capacity drop

ROSINI, Massimiliano Daniele
2015

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.
2015
Andreianov, Boris; Donadello, Carlotta; Razafison, Ulrich; Rosini, Massimiliano Daniele
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/2356635
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