Page 466 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 466
ANALYSIS OF PDES ON NETWORKS (MS-26)
Macroscopic traffic flow models on road networks
Paola Goatin, paola.goatin@inria.fr
Inria, France
The talk will review the main macroscopic models of vehicular traffic flow on networks, focus-
ing on the description of dynamics at junctions. I will then show some optimal control appli-
cation, as well as some recent developments accounting for the impact of modern navigation
systems.
First order Mean Field Games on networks
Claudio Marchi, marchi@math.unipd.it
University of Padova, Italy
Coauthors: Yves Achdou, Paola Mannucci, Nicoletta Tchou
The theory of Mean Field Games studies the asymptotic behaviour of differential games (mainly
in terms of their Nash equilibria) as the number of players tends to infinity. In these games, the
players are rational and indistinguishable: each player aims at choosing its trajectory so to
minimize a cost which depends on the trajectory itself and on the distribution of the whole
population of agents. We focus our attention on deterministic Mean Field Games with finite
horizon in which the states of the players are constrained in a network (in our setting, a network
is given by a finite collection of vertices connected by continuous edges which cannot self-
intersect). In these games, an agent can control its dynamics and has to pay a cost formed by
a running cost depending on the evolution of the distribution of all agents and a terminal cost
depending on the distribution of all agents at terminal time. As in the Lagrangian approach, we
introduce a relaxed notion of Mean Field Games equilibria and we shall deal with probability
measures on trajectories on the network instead of probability measures on the network. This
is a joint work with: Y. Achdou (Univ. of Paris), P. Mannucci (Univ. of Padova) and N. Tchou
(Univ. of Rennes).
Spectral minimal partitions on metric graphs, and applications
Delio Mugnolo, deliomu@gmail.com
University of Hagen, Germany
There exist several possibilities of partitioning graphs or manifolds, including those based on
Cheeger cuts or nodal domains. We present a different approach that elaborates on a theory
developed in the last 15 years, among others, by Bonnaillie-Noël, Helffer, Hoffmann-Ostenhof,
and Terracini. While these authors focus on domains, we are going to discuss the partitioning
of metric graphs in terms of spectral quantities of the associated Laplacian.
We introduce a well-defined class of spectral partitions of metric graphs and show some of
their features. While the complicated topology of metric graphs prevents us from recovering all
results that hold for domains, new remarkable features also arise.
This is joint work with Matthias Hofmann, James Kennedy, Pavel Kurasov, Corentin Léna,
Marvin Plümer.
464
Macroscopic traffic flow models on road networks
Paola Goatin, paola.goatin@inria.fr
Inria, France
The talk will review the main macroscopic models of vehicular traffic flow on networks, focus-
ing on the description of dynamics at junctions. I will then show some optimal control appli-
cation, as well as some recent developments accounting for the impact of modern navigation
systems.
First order Mean Field Games on networks
Claudio Marchi, marchi@math.unipd.it
University of Padova, Italy
Coauthors: Yves Achdou, Paola Mannucci, Nicoletta Tchou
The theory of Mean Field Games studies the asymptotic behaviour of differential games (mainly
in terms of their Nash equilibria) as the number of players tends to infinity. In these games, the
players are rational and indistinguishable: each player aims at choosing its trajectory so to
minimize a cost which depends on the trajectory itself and on the distribution of the whole
population of agents. We focus our attention on deterministic Mean Field Games with finite
horizon in which the states of the players are constrained in a network (in our setting, a network
is given by a finite collection of vertices connected by continuous edges which cannot self-
intersect). In these games, an agent can control its dynamics and has to pay a cost formed by
a running cost depending on the evolution of the distribution of all agents and a terminal cost
depending on the distribution of all agents at terminal time. As in the Lagrangian approach, we
introduce a relaxed notion of Mean Field Games equilibria and we shall deal with probability
measures on trajectories on the network instead of probability measures on the network. This
is a joint work with: Y. Achdou (Univ. of Paris), P. Mannucci (Univ. of Padova) and N. Tchou
(Univ. of Rennes).
Spectral minimal partitions on metric graphs, and applications
Delio Mugnolo, deliomu@gmail.com
University of Hagen, Germany
There exist several possibilities of partitioning graphs or manifolds, including those based on
Cheeger cuts or nodal domains. We present a different approach that elaborates on a theory
developed in the last 15 years, among others, by Bonnaillie-Noël, Helffer, Hoffmann-Ostenhof,
and Terracini. While these authors focus on domains, we are going to discuss the partitioning
of metric graphs in terms of spectral quantities of the associated Laplacian.
We introduce a well-defined class of spectral partitions of metric graphs and show some of
their features. While the complicated topology of metric graphs prevents us from recovering all
results that hold for domains, new remarkable features also arise.
This is joint work with Matthias Hofmann, James Kennedy, Pavel Kurasov, Corentin Léna,
Marvin Plümer.
464
