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We provide a numerical realisation of an optimal control problem for pedestrian motion with agents that was analysed in Herzog, Pietschmann, Winkler: "Optimal Control of Hughes' Model for Pedestrian Flow via Local Attraction.", arXiv 2011.03580, 2020.
“A continuum theory for the flow of pedestrians”
Roger. Hughes · 2002
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“The use of classical Lax-Friedrichs Riemann solvers with discontinuous Galerkin methods” ICFD Conference on Numerical Methods for Fluid Dynamics, Part II (Oxford, 2001)
W.. Rider and R.. Lowrie · 2002
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“A finite volume scheme for the Patlak–Keller–Segel chemotaxis model”
Francis Filbet · 2006
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“Optimal L p L^{p} - L q L^{q} -estimates for parabolic boundary value problems with inhomogeneous data”
Robert Denk, Matthias Hieber and Jan Pr\"uss · 2007
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“New Interior Penalty Discontinuous Galerkin Methods for the Keller–Segel Chemotaxis Model”
Yekaterina Epshteyn and Alexander Kurganov · 2009
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“On the Hughes’ model for pedestrian flow: The one-dimensional case”
Marco Di, Peter. Markowich, Jan-Frederik Pietschmann and Marie-Therese Wolfram · 2010
Earlier work this paper cites.
“A Flux-Corrected Finite Element Method for Chemotaxis Problems”
R. Strehl, A. Sokolov, D. Kuzmin and S. Turek · 2010
Earlier work this paper cites.
“Optimal Control of Hughes’ Model for Pedestrian Flow via Local Attraction”, 2020
Roland Herzog, Jan-Frederik Pietschmann and Max Winkler · 2011
Earlier work this paper cites.
“The one-dimensional Hughes model for pedestrian flow: Riemann-type solutions”
Debora Amadori and M. Di · 2012
Earlier work this paper cites.
“Mathematical Aspects of Discontinuous Galerkin Methods”
Daniele Di and Alexandre Ern · 2012
Earlier work this paper cites.
“Sparse stabilization and optimal control of the Cucker-Smale model”
Marco Caponigro, Massimo Fornasier, Benedetto Piccoli and Emmanuel Tr\’elat · 2013
Earlier work this paper cites.
“On entropy weak solutions of Hughes’ model for pedestrian motion”
Nader El-Khatib, Paola Goatin and Massimiliano. Rosini · 2013
Cited alongside, same era.
“Existence results for Hughes’ model for pedestrian flows”
Debora Amadori, Paola Goatin and Massimiliano. Rosini · 2014
Cited alongside, same era.
“Coupling traffic flow networks to pedestrian motion”
R. Borsche, A. Klar, S. K\"uhn and A. Meurer · 2014
Cited alongside, same era.
“Mean field games with nonlinear mobilities in pedestrian dynamics”
Martin Burger, Marco Di, Peter. Markowich and Marie-Therese Wolfram · 2014
Cited alongside, same era.
“Explicit flock solutions for Quasi-Morse potentials”
J.. Carillo, Y. Huang and S. Martin · 2014
Cited alongside, same era.
“On the efficacy of a control volume finite element method for the capture of patterns for a volume-filling chemotaxis model”
“A Boltzmann approach to mean-field sparse feedback control”
Giacomo Albi, Massimo Fornasier and Dante Kalise · 2017
Later among the works it cites.
“Deterministic particle approximation of the Hughes model in one space dimension”
Marco Di, Simone Fagioli, Massimiliano Rosini and Giovanni Russo · 2017
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“Local Discontinuous Galerkin Method for the Keller-Segel Chemotaxis Model”
Xingjie Li, Chi-Wang Shu and Yang Yang · 2017
Later among the works it cites.
“Microscopic and macroscopic models for coupled car traffic and pedestrian flow”
R. Borsche and A. Meurer · 2018
Later among the works it cites.
“Modeling crowd dynamics through hyperbolic-elliptic equations”
Rinaldo. Colombo, Maria Gokieli and Massimiliano. Rosini · 2018
Later among the works it cites.
“Energy Dissipative Local Discontinuous Galerkin Methods for Keller–Segel Chemotaxis Model”
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Moustafa Ibrahim and Mazen Saad · 2014
Cited alongside, same era.
“Differential equations modeling crowd interactions”
Raul Borsche, Rinaldo. Colombo, Mauro Garavello and Anne Meurer · 2015
Cited alongside, same era.
“Invisible Control of Self-Organizing Agents Leaving Unknown Environments”
Giacomo Albi, Mattia Bongini, Emiliano Cristiani and Dante Kalise · 2016
Cited alongside, same era.
Martin Burger et al · 2016
Cited alongside, same era.
“A semi-Lagrangian scheme for a modified version of the Hughes’ model for pedestrian flow”
Elisabetta Carlini, Adriano Festa, Francisco. Silva and Marie-Therese Wolfram · 2016
Cited alongside, same era.
“An improved version of the Hughes model for pedestrian flow”
Jose. Carrillo, Stephan Martin and Marie-Therese Wolfram · 2016
Cited alongside, same era.
Li Guo, Xingjie Li and Yang Yang · 2018
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“Interacting particles and optimization”
Ren\’e Pinnau and Claudia Totzeck · 2018
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“Recent Developments in Controlled Crowd Dynamics”
M.. Banda, M. Herty and T. Trimborn · 2020
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Constantin Christof and Gerd Wachsmuth · 2021
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“Optimal Control through Leadership of the Cucker and Smale Flocking Model with Time Delays”
Adsadang Himakalasa and Suttida Wongkaew · 2021
Later among the works it cites.