Riemann problems with non--local point constraints and capacity drop

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 applicati...

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Bibliographic Details
Main Authors: Boris Andreianov, Carlotta Donadello, Ulrich Razafison, Massimiliano D. Rosini
Format: Article
Language:English
Published: AIMS Press 2014-11-01
Series:Mathematical Biosciences and Engineering
Subjects:
loss of uniqueness
riemann problem
crowd dynamics
loss of self > similarity
capacity drop.
non > local constrained hyperbolic pde's
Online Access:https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.259
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Summary: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.
ISSN:1551-0018

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