25 Maggio, 2017 15:15 oclock

Sezione di Probabilità e Statistica Matematica

A probabilistic view of the inelastic Boltzmann equation and generalized Kac equations

Federico Bassetti, Dipartimento di Matematica, Università degli Studi di Pavia

Sala Maestrale, Tender, piano -1

In this talk we present an overview of some results obtained on a class
of measure-valued nonlinear kinetic-type equations. We shall show how
suitable probabilistic techniques, essentially related to central limit
theorems and fixed point equations for distributions, can be fruitfully
used to study these equations. In the first part of the talk, we shall
briefly discuss existence, shape and dynamical stability of equilibria
for the class of one dimensional
generalized Kac equations, whose collisional operator is expressed in
term of a smoothing transformation.
This class of equations includes the well-known Kac model as well its
generalisation to inelastic collisions and also various models used in
econophysic.
In the second part of the talk we will show how the previous results
(partially) extend to the multidimensional homogeneous inelastic
Boltzmann equation.

The talk is based on some joint works with L. Ladelli, D. Matthes, E.
Perversi, E. Regazzini, and G. Toscani.