Fetching the paper…
Reading the bibliography…
We provide an overview of the results on Hughes' model for pedestrian movements available in the literature.
On kinematic waves. II. A theory of traffic flow on long crowded roads
M. Lighthill and G. Whitham · 1955
Earlier work this paper cites.
Shock waves on the highway
P. I. Richards · 1956
Earlier work this paper cites.
First order quasilinear equations with several independent variables
S. N. Kruzhkov · 1970
Earlier work this paper cites.
Polygonal approximations of solutions of the initial value problem for a conservation law
C. M. Dafermos · 1972
Earlier work this paper cites.
First order quasilinear equations with boundary conditions
C. Bardos, A. Y. le Roux, and J.-C. Nédélec · 1979
Earlier work this paper cites.
Hyperbolic systems of conservation laws
A. Bressan · 2000
Earlier work this paper cites.
Strong traces for solutions of multidimensional scalar conservation laws
A. Vasseur · 2001
Earlier work this paper cites.
A continuum theory for the flow of pedestrians
R. L. Hughes · 2002
Earlier work this paper cites.
Hyperbolic systems of conservation laws
P. G. LeFloch · 2002
Earlier work this paper cites.
Traffic flow on networks
M. Garavello and B. Piccoli · 2006
Earlier work this paper cites.
Existence of strong traces for quasi-solutions of multidimensional conservation laws
E. Y. Panov · 2007
Earlier work this paper cites.
Revisiting Hughes’ dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm
L. Huang, S. Wong, M. Zhang, C.-W. Shu, and W. H. Lam · 2009
Earlier work this paper cites.
Existence and strong pre-compactness properties for entropy solutions of a first-order quasilinear equation with discontinuous flux
E. Y. Panov · 2010
Earlier work this paper cites.
On the Hughes’ model for pedestrian flow: the one-dimensional case
M. Di Francesco, P. A. Markowich, J.-F. Pietschmann, and M.-T. Wolfram · 2011
Earlier work this paper cites.
The one-dimensional Hughes model for pedestrian flow: Riemann-type solutions
D. Amadori and M. Di Francesco · 2012
Earlier work this paper cites.
On entropy weak solutions of Hughes’ model for pedestrian motion
N. El-Khatib, P. Goatin, and M. D. Rosini · 2013
Earlier work this paper cites.
The wave-front tracking algorithm for Hughes’ model of pedestrian motion
P. Goatin and M. Mimault · 2013
Earlier work this paper cites.
Macroscopic models for vehicular flows and crowd dynamics: theory and applications
M. D. Rosini · 2013
Earlier work this paper cites.
Existence results for Hughes’ model for pedestrian flows
D. Amadori, P. Goatin, and M. D. Rosini · 2014
Cited alongside, same era.
Crowd dynamics and conservation laws with nonlocal constraints and capacity drop
B. Andreianov, C. Donadello, and M. D. Rosini · 2014
Cited alongside, same era.
Coupling traffic flow networks to pedestrian motion
R. Borsche, A. Klar, S. Kühn, and A. Meurer · 2014
Cited alongside, same era.
Interaction of road networks and pedestrian motion at crosswalks
R. Borsche and A. Meurer · 2014
Cited alongside, same era.
Mean field games with nonlinear mobilities in pedestrian dynamics
M. Burger, M. Di Francesco, P. A. Markowich, and M.-T. Wolfram · 2014
Cited alongside, same era.
On the micro-macro limit in traffic flow
R. M. Colombo and E. Rossi · 2014
Cited alongside, same era.
Follow-the-leader approximations of macroscopic models for vehicular and pedestrian flows
M. Di Francesco, S. Fagioli, M. Rosini, and G. Russo · 2017
Later among the works it cites.
Deterministic particle approximation of the Hughes model in one space dimension
M. Di Francesco, S. Fagioli, M. D. Rosini, and G. Russo · 2017
Later among the works it cites.
Modeling crowd dynamics through hyperbolic-elliptic equations
R. M. Colombo, M. Gokieli, and M. D. Rosini · 2018
Later among the works it cites.
A deterministic particle approximation for non-linear conservation laws
M. Di Francesco, S. Fagioli, M. D. Rosini, and G. Russo · 2018
Later among the works it cites.
Crowd dynamics. Vol. 1. Theory, models, and safety problems
L. Gibelli and N. Bellomo, editors · 2018
Later among the works it cites.
The continuum limit of Follow-the-Leader models—a short proof
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Scalar conservation law with discontinuity arising in pedestrian modeling
M. Mimault · 2014
Cited alongside, same era.
Macroscopic modeling and simulations of room evacuation
M. Twarogowska, P. Goatin, and R. Duvigneau · 2014
Cited alongside, same era.
Rigorous derivation of nonlinear scalar conservation laws from follow-the-leader type models via many particle limit
M. Di Francesco and M. Rosini · 2015
Cited alongside, same era.
Invisible control of self-organizing agents leaving unknown environments
G. Albi, M. Bongini, E. Cristiani, and D. Kalise · 2016
Cited alongside, same era.
Qualitative behaviour and numerical approximation of solutions to conservation laws with non-local point constraints on the flux and modeling of crowd dynamics at the bottlenecks
B. Andreianov, C. Donadello, U. Razafison, and M. D. Rosini · 2016
Cited alongside, same era.
M. Burger, R. Pinnau, A. Roth, C. Totzeck, and O. Tse · 2016
Cited alongside, same era.
H. Holden and N. H. Risebro · 2018
Later among the works it cites.
Follow-the-leader models can be viewed as a numerical approximation to the Lighthill-Whitham-Richards model for traffic flow
H. Holden and N. H. Risebro · 2018
Later among the works it cites.
A macroscopic model to reproduce self-organization at bottlenecks
B. Andreianov and A. Sylla · 2020
Later among the works it cites.
A unified multiscale vision of behavioral crowds
B. Aylaj, N. Bellomo, L. Gibelli, and A. Reali · 2020
Later among the works it cites.
Convergence of the follow-the-leader scheme for scalar conservation laws with space dependent flux
M. Di Francesco and G. Stivaletta · 2020
Later among the works it cites.
Crowd dynamics. Vol. 2–theory, models, and applications
L. Gibelli, editor · 2020
Later among the works it cites.
A numerical scheme for evacuation dynamics
M. Gokieli and A. Szczepańczyk · 2020
Later among the works it cites.
Optimal control of hughes’ model for pedestrian flow via local attraction, 2020
R. Herzog, J.-F. Pietschmann, and M. Winkler · 2020
Later among the works it cites.
On existence, stability and many-particle approximation of solutions of 1D Hughes model with linear costs, 2021
B. Andreianov, M. Rosini, and G. Stivaletta · 2021
Later among the works it cites.
Crowd Dynamics. Vol. 3
L. Gibelli and N. Bellomo, editors · 2021
Later among the works it cites.
Existence of solutions to a class of one-dimensional models for pedestrian evacuations
B. Andreianov and T. Girard · 2023
Closest in time.
Numerical investigation of agent controlled pedestrian dynamics using a structure preserving finite volume scheme, 2023
J.-F. Pietschmann, A. Stötzner, and M. Winkler · 2023
Closest in time.