70 citations · 433 across the 44 of their papers we have counts for
7 papers · 1 filter
Derivation and analysis of continuum models for crossing pedestrian traffic
Sabine Hittmeir, Helene Ranetbauer, Christian Schmeiser +1
In this paper we study hyperbolic and parabolic nonlinear partial differential equation models, which describe the evolution of two intersecting pedestrian flows. We assume that in…
Kinetic description of collision avoidance in pedestrian crowds by sidestepping
Adriano Festa, Andrea Tosin, Marie-Therese Wolfram
In this paper we study a kinetic model for pedestrians, who are assumed to adapt their motion towards a desired direction while avoiding collisions with others by stepping aside. T…
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…
Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms
José A. Carrillo, Helene Ranetbauer, Marie-Therese Wolfram
In this paper we present a numerical scheme for nonlinear continuity equations, which is based on the gradient flow formulation of an energy functional with respect to the quadrati…
Balanced growth path solutions of a Boltzmann mean field game model for knowledge growth
Martin Burger, Alexander Lorz, Marie-Therese Wolfram
In this paper we study balanced growth path solutions of a Boltzmann mean field game model proposed by Lucas et al [13] to model knowledge growth in an economy. Agents can either i…
Parabolic free boundary price formation models under market size fluctuations
Peter A. Markowich, Josef Teichmann, Marie-Therese Wolfram
In this paper we propose an extension of the Lasry-Lions price formation model which includes fluctuations of the numbers of buyers and vendors. We analyze the model in the case of…
A Semi-Lagrangian scheme for a modified version of the Hughes model for pedestrian flow
Elisabetta Carlini, Adriano Festa, Francisco J. Silva +1
In this paper we present a Semi-Lagrangian scheme for a regularized version of the Hughes model for pedestrian flow. Hughes originally proposed a coupled nonlinear PDE system descr…