58 citations · 85 across the 8 of their papers we have counts for
5 papers · 1 filter
The mathematical theory of Hughes' model: a survey of results
Debora Amadori, Boris Andreianov, Marco Di Francesco +9
We provide an overview of the results on Hughes' model for pedestrian movements available in the literature. After the first successful approaches to solving a regularised version…
Cross-diffusion systems with excluded volume effects and asymptotic gradient flows
Maria Bruna, Martin Burger, Helene Ranetbauer +1
In this paper we discuss the analysis of a cross-diffusion PDE system for a mixture of hard spheres, which was derived by Bruna and Chapman from a stochastic system of interacting…
A local version of the Hughes model for pedestrian flow
José A. Carrillo, Stephan Martin, Marie-Therese Wolfram
Roger Hughes proposed a macroscopic model for pedestrian dynamics, in which individuals seek to minimize their travel time but try to avoid regions of high density. One of the basi…
Socio-economic applications of finite state mean field games
Diogo A. Gomes, Roberto M. Velho, Marie-Therese Wolfram
In this paper we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or the con…
A Drift-Diffusion-Reaction Model for Excitonic Photovoltaic Bilayers: Asymptotic Analysis and A 2-D HDG Finite-Element Scheme
Daniel Brinkman, Klemens Fellner, Peter A. Markowich +1
We present and discuss a mathematical model for the operation of bilayer organic photovoltaic devices. Our model couples drift-diffusion-recombination equations for the charge carr…