In this talk I will present some results concerning the well-posedness and asymptotic behaviour of some evolution equations arising in social sciences naturally involving measure-valued functions. More precisely I will present some models of opinion formation. Imagine a group of individuals debating over some question. As a result of interactions among individuals, the distribution of opinion, a priori a general probability measure, is not static but evolves in time. The problem is then to study the long-time behaviour of this distibution assuming some knowledge about the way people interact. This amounts to study the aymptotic behaviour of some transport equation for measure-valued function. We obtain the asymptotic behaviour of the solution and an estimation of the rate of convergence in terms of a Monge-Kantorovich distance.

In this talk I will present some results concerning the well-posedness and asymptotic behaviour of some evolution equations arising in social sciences naturally involving measure-valued functions. More precisely I will present some models of opinion formation. Imagine a group of individuals debating over some question. As a result of interactions among individuals, the distribution of opinion, a priori a general probability measure, is not static but evolves in time. The problem is then to study the long-time behaviour of this distibution assuming some knowledge about the way people interact. This amounts to study the aymptotic behaviour of some transport equation for measure-valued function. We obtain the asymptotic behaviour of the solution and an estimation of the rate of convergence in terms of a Monge-Kantorovich distance.