Fetching the paper…
Reading the bibliography…
In this paper, we present a new generalized Hughes model designed to intelligently depict pedestrian congestion dynamics, allowing pedestrian groups to either navigate through or circumvent high-density regions.
Differential games: A mathematical theory with applications to warfare and pursuit, control and optimization, 1965
Rufus Isaacs · 1965
Earlier work this paper cites.
Viscosity solutions of fully nonlinear second-order elliptic partial differential equations
Hitoshi Ishii and Pierre-Luis Lions · 1990
Earlier work this paper cites.
User’s guide to viscosity solutions of second order partial differential equations
Michael G Crandall, Hitoshi Ishii, and Pierre-Louis Lions · 1992
Earlier work this paper cites.
Social force model for pedestrian dynamics
Dirk Helbing and Peter Molnar · 1995
Earlier work this paper cites.
Nonlinear parabolic equations with measure data
Lucio Boccardo, Andrea Dall’Aglio, Thierry Gallouët, and Luigi Orsina · 1997
Earlier work this paper cites.
Simulating dynamical features of escape panic
Dirk Helbing, Illés Farkas, and Tamas Vicsek · 2000
Earlier work this paper cites.
Simulation of pedestrian dynamics using a two-dimensional cellular automaton
Carsten Burstedde, Kai Klauck, Andreas Schadschneider, and Johannes Zittartz · 2001
Earlier work this paper cites.
A continuum theory for the flow of pedestrians
Roger L Hughes · 2002
Earlier work this paper cites.
Controlled Markov processes and viscosity solutions
Wendell H. Fleming and H. Mete Soner · 2006
Earlier work this paper cites.
Jeux à champ moyen. I − \displaystyle\text{I}- le cas stationnaire
Jean-Michel Lasry and Pierre-Louis Lions · 2006
Earlier work this paper cites.
Jeux à champ moyen. II − \displaystyle\text{II}- horizon fini et contrôle optimal
Jean-Michel Lasry and Pierre-Louis Lions · 2006
Earlier work this paper cites.
Large population stochastic dynamic games: closed-loop mckean-vlasov systems and the nash certainty equivalence principle
Peter E Caines, Minyi Huang, and Roland P Malhamé · 2006
Earlier work this paper cites.
Mean field games
Jean-Michel Lasry and Pierre-Louis Lions · 2007
Earlier work this paper cites.
Large-population cost-coupled lqg problems with nonuniform agents: individual-mass behavior and decentralized ε \displaystyle\varepsilon -nash equilibria
Minyi Huang, Peter E Caines, and Roland P Malhamé · 2007
Earlier work this paper cites.
Revisiting hughes’ dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm
Ling Huang, SC Wong, Mengping Zhang, Chi-Wang Shu, and William HK Lam · 2009
Earlier work this paper cites.
Mean field games: numerical methods
Yves Achdou and Italo Capuzzo-Dolcetta · 2010
Earlier work this paper cites.
Partial differential equations
Lawrence C Evans · 2010
Earlier work this paper cites.
Continuous limit of a crowd motion and herding model: analysis and numerical simulations
Martin Burger, Peter Markowich, and Jan-Frederik Pietschmann · 2011
Earlier work this paper cites.
On a mean field game approach modeling congestion and aversion in pedestrian crowds
Aimé Lachapelle and Marie-Therese Wolfram · 2011
Earlier work this paper cites.
Mean field games in economics, 2012
B Moll · 2012
Earlier work this paper cites.
From the microscale to collective crowd dynamics
Nicola Bellomo, Abdelghani Bellouquid, and Damian Knopoff · 2013
Earlier work this paper cites.
Mean field games with nonlinear mobilities in pedestrian dynamics
Martin Burger, Marco Di Francesco, Peter A Markowich, and Marie-Therese Wolfram · 2014
Earlier work this paper cites.
Macroscopic modeling and simulations of room evacuation
Monika Twarogowska, Paola Goatin, and Regis Duvigneau · 2014
Cited alongside, same era.
Partial differential equation models in macroeconomics
Yves Achdou, Francisco J Buera, Jean-Michel Lasry, Pierre-Louis Lions, and Benjamin Moll · 2014
Cited alongside, same era.
On the planning problem for the mean field games system
Alessio Porretta · 2014
Cited alongside, same era.
On multiscale models of pedestrian crowds from mesoscopic to macroscopic
Nicola Bellomo and Abdelghani Bellouquid · 2015
Cited alongside, same era.
Weak solutions to fokker–planck equations and mean field games
Alessio Porretta · 2015
Cited alongside, same era.
Time-dependent mean-field games with logarithmic nonlinearities
Diogo A Gomes and Edgard Pimentel · 2015
Cited alongside, same era.
Optimal control of hughes’ model for pedestrian flow via local attraction
Roland Herzog, Jan-Frederik Pietschmann, and Max Winkler · 2020
Later among the works it cites.
On quasi-stationary mean field games models
Charafeddine Mouzouni · 2020
Later among the works it cites.
Short-time existence for a general backward–forward parabolic system arising from mean-field games
Marco Cirant, Roberto Gianni, and Paola Mannucci · 2020
Later among the works it cites.
Extended mean-field games
Pierre-Louis Lions and Panagiotis E Souganidis · 2020
Later among the works it cites.
An introduction to mean field game theory
Yves Achdou, Pierre Cardaliaguet, François Delarue, Alessio Porretta, Filippo Santambrogio, Pierre Cardaliaguet, and Alessio Porretta · 2020
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Time-dependent mean-field games in the subquadratic case
Diogo A Gomes, Edgard A Pimentel, and Héctor Sánchez-Morgado · 2015
Cited alongside, same era.
Second order mean field games with degenerate diffusion and local coupling
Pierre Cardaliaguet, P Jameson Graber, Alessio Porretta, and Daniela Tonon · 2015
Cited alongside, same era.
An improved version of the hughes model for pedestrian flow
Jose A Carrillo, Stephan Martin, and Marie-Therese Wolfram · 2016
Cited alongside, same era.
Convergence of a finite difference scheme to weak solutions of the system of partial differential equations arising in mean field games
Yves Achdou and Alessio Porretta · 2016
Cited alongside, same era.
Time-dependent mean-field games in the superquadratic case
Diogo A Gomes, Edgard Pimentel, and Héctor Sánchez-Morgado · 2016
Cited alongside, same era.
Mean-field type modeling of nonlocal crowd aversion in pedestrian crowd dynamics
Alexander Aurell and Boualem Djehiche · 2018
Cited alongside, same era.
A continuum model for pedestrian flow with explicit consideration of crowd force and panic effects
Haoyang Liang, Jie Du, and Sze Chun Wong · 2021
Later among the works it cites.
Maximal L q − \displaystyle\text{L}^{q}- regularity for parabolic hamilton-jacobi equations and applications to mean field games
Marco Cirant and Alessandro Goffi · 2021
Later among the works it cites.
Towards a mathematical theory of behavioral human crowds
Nicola Bellomo, Livio Gibelli, Annalisa Quaini, and Alessandro Reali · 2022
Later among the works it cites.
Income and wealth distribution in macroeconomics: A continuous-time approach
Yves Achdou, Jiequn Han, Jean-Michel Lasry, Pierre-Louis Lions, and Benjamin Moll · 2022
Later among the works it cites.
Existence and non-existence for time-dependent mean field games with strong aggregation
Marco Cirant and Daria Ghilli · 2022
Later among the works it cites.
A variational approach to first order kinetic mean field games with local couplings
Megan Griffin-Pickering and Alpár R Mészáros · 2022
Later among the works it cites.
Classical and weak solutions to local first-order mean field games through elliptic regularity
Sebastian Muñoz · 2022
Later among the works it cites.
Human behavioral crowds review, critical analysis, and research perspectives
Nicola Bellomo, Jie Liao, Annalisa Quaini, Lucia Russo, and Costantinos Siettos · 2023
Closest in time.
Kinetic modeling of a leader–follower system in crowd evacuation with collective learning
Jie Liao, Yi’ang Ren, and Wenbin Yan · 2023
Closest in time.
Jan-Frederik Pietschmann, Ailyn Stötzner, and Max Winkler · 2023
Closest in time.
The mathematical theory of hughes’ model: a survey of results
Debora Amadori, Boris Andreianov, Marco Di Francesco, Simone Fagioli, Théo Girard, Paola Goatin, Peter Markowich, Jan F Pietschmann, Massimiliano D Rosini, Giovanni Russo, et al · 2023
Closest in time.
Discrete approximation of stationary mean field games
Tigran Bakaryan, Diogo Gomes, and Héctor Sánchez Morgado · 2023
Closest in time.
On quasi-stationary mean field games of controls
Fabio Camilli and Claudio Marchi · 2023
Closest in time.
Classical solutions to local first-order extended mean field games
Sebastian Munoz · 2023
Closest in time.
Regularizing effects of the entropy functional in optimal transport and planning problems
Alessio Porretta · 2023
Closest in time.
Stability analysis of the non-separable mean-fields games for pedestrian flow in large corridors
Mohamed Ghattassi, Nader Masmoudi, and Eliot Pacherie · 2023
Closest in time.