Tuesday, 2 February 2016, 3 p.m. (sharp), Prof. Alessio Porretta, Università di Roma Tor Vergata, at the conference room of IMATI-CNR in Pavia, will give a lecture titled:
On the systems of PDE in mean field games theory
and at 4 p.m. Dr. Giuliano Lazzaroni, SISSA, Trieste, at the conference room of IMATI-CNR in Pavia, will give a lecture titled:
Dynamic fracture: existence and uniqueness of evolutions for a simplified peeling test
as part of the Applied Mathematics Seminar (IMATI-CNR and Dipartimento di Matematica, Pavia).
At the end a refreshment will be organized.
Mean field games theory was introduced by J-M. Lasry and P.-L. Lions
as a model for describing strategic interactions in the dynamics of
populations of several identical agents whenever the individual
optimization criteria depend on the collective behavior. A mean field
approach leads to a macroscopic model where Nash equilibria are
interpreted as solutions of a system of PDEs, in which a backward
Bellman equation for the individual strategy is strongly coupled with
a forward Fokker-Planck equation for the mass distribution law. I will
describe several features of those coupled systems, which bring new
PDE issues as well as new connections with optimal control and
We present a simplified model of dynamic crack propagation, where the
equation of elastodynamics is coupled with Griffith's principle. In recent
years there has been an increasing interest in studying systems where
rate-dependent equations are coupled with rate-independent flow rules.
Despite a number of papers devoted to regularised models, only partial
results are available for dynamic fracture and heavy mathematical
difficulties have to be overcome. In our work we deal with a problem of
debonding propagation for a one-dimensional thin film, partially glued on a
substrate and subject to oscillations in the debonded part. We provide
existence and uniqueness results for dynamic evolutions and study the limit
as the speed of external loading tends to zero. We establish the properties
of the limit solution and see that in general it does not coincide with the
expected quasistatic limit.
Joint collaboration with Gianni Dal Maso and Lorenzo Nardini (SISSA).
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