Abstract:
We study several variants of the so-called Hughes model for pedestrian flows. Those combine a non linear continuity equation with a Hamilton-Jacobi equation of the eikonal type. The study of those models has so far only been possible when sufficient viscosity was added to both the evolution equation on the density and the Hamilton-Jacobi. Using new compactness estimates, we show how to remove such artificial viscosity.
This is a joint work with D. Gomez and P. Markowich. |