Mean field games with nonlinear mobilities in pedestrian dynamics

Beitrag in einer Fachzeitschrift


Details zur Publikation

Autorinnen und Autoren: Burger M, Di Francesco M, Markowich PA, Wolfram MT
Zeitschrift: Discrete and Continuous Dynamical Systems-Series B
Jahr der Veröffentlichung: 2014
Band: 19
Seitenbereich: 1311-1333
ISSN: 1531-3492
Sprache: Englisch


Abstract

In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is determined by minimizing a cost functional, which depends on his/her position, velocity, exit time and the overall density of people. This microscopic setup leads in the mean-field limit to a parabolic optimal control problem. We discuss the modeling of the macroscopic optimal control approach and show how the optimal conditions relate to the Hughes model for pedestrian flow. Furthermore we provide results on the existence and uniqueness of minimizers and illustrate the behavior of the model with various numerical results.


Einrichtungen weiterer Autorinnen und Autoren

King Abdullah University of Science and Technology (KAUST) / جامعة الملك عبد الله للعلوم و التقنية
Medizinische Universität Wien
University of Bath
Westfälische Wilhelms-Universität (WWU) Münster


Zitierweisen

APA:
Burger, M., Di Francesco, M., Markowich, P.A., & Wolfram, M.-T. (2014). Mean field games with nonlinear mobilities in pedestrian dynamics. Discrete and Continuous Dynamical Systems-Series B, 19, 1311-1333. https://dx.doi.org/10.3934/dcdsb.2014.19.1311

MLA:
Burger, Martin, et al. "Mean field games with nonlinear mobilities in pedestrian dynamics." Discrete and Continuous Dynamical Systems-Series B 19 (2014): 1311-1333.

BibTeX: 

Zuletzt aktualisiert 2018-03-12 um 16:08