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 [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.
Cite
@article{arxiv.1403.4203,
title = {Riemann problems with non--local point constraints and capacity drop},
author = {Boris Andreianov and Carlotta Donadello and Ulrich Razafison and Massimiliano D. Rosini},
journal= {arXiv preprint arXiv:1403.4203},
year = {2014}
}
Comments
19 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1304.6282