A fluid-dynamic model for the movement of pedestrians.

*(English)*Zbl 0776.92016Summary: A fluid-dynamic description for the collective movement of pedestrians is developed on the basis of a Boltzmann-like gas-kinetic model. The differences between these pedestrian-specific equations and those for ordinary fluids are worked out; they concern, for example, the mechanism of relaxation to equilibrium, the role of “pressure”, the special influence of internal friction, and the origin of “temperature”.

Some interesting results are derived that can be compared to real situations — for example, the development of walking lanes and of pedestrian jams, the propagation of waves, and behavior on a dance floor. Possible applications of the model to town- and traffic-planning are outlined.

##### MSC:

92F05 | Applications of mathematics to other natural sciences |

76Z99 | Biological fluid mechanics |

76P05 | Rarefied gas flows, Boltzmann equation |

92C05 | Biophysics |