Technion - Israel Institute of Technology
 
          Department of Mathematics
 
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     PDE AND APPLIED MATHEMATICS SEMINAR
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DATE: Tuesday, November 15, 2011
 
SPEAKER: Magali Mercier-Lecureox, Technion
 
TITLE: Nonlocal scalar conservation laws in the modeling of
pedestrian traffic
 
PLACE: Room 814, Amado Mathematics Building, Technion
 
TIME: 14:30
 
ABSTRACT:  In this talk, we are interested in the
modeling of pedestrian traffic. In a macroscopic
setting, we are led to consider a conservation law on
the density of the pedestrians. A variety of models are
possible through the choice of the pedestrian speed.
Here, we assume the speed depends on the position of the
pedestrian and on the local density, but also on the
entire distribution of the pedestrians' density. More
precisely, we assume the pedestrians' speed depends on
the average of the density around a given point. If
furthermore there are several populations, we must add
as many equations as the number of different populations
and we have to wonder how to modelize the interaction
between the populations. On the analytical point of
view, we have finally to deal with a system of
conservation laws with a nonlocal flow.
 
I want here to present these models and study their
properties, in particular, using either Kruzkov theory
on scalar conservation laws or optimal transport tools,
I will prove existence and uniqueness of weak solutions
for these models.
 
For further info: 
Yehuda Pinchover   <pincho@techunix.technion.ac.il> 
 
For past and future Applied Math/PDE seminars see:
 <http://www.math.technion.ac.il/pde/seminar.html>
 
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Technion Math. Net (TECHMATH)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Yehuda Pinchover   <pincho@tx.technion.ac.il>