Seminario di Equazioni Differenziali e Applicazioni: “Viscosity solutions of an Hamilton-Jacobi Equation in Wasserstein spaces and applications”

Lunedì 8 Gennaio 2018, ore 12:30 - Aula 2BC30 - Antonio Marigonda


Lunedì 8 Gennaio 2018 alle ore 12:30 in Aula 2BC30, Antonio Marigonda (Università di Verona) terrà un seminario dal titolo “Viscosity solutions of an Hamilton-Jacobi Equation in Wasserstein spaces and applications”.

In this talk we present recent results about the characterization of the value function for a class of control problems and differential games in the Wasserstein space as the unique solution of and infinite-dimensional Hamilton-Jacobi equation in a suitable viscosity sense. Such an equation arises naturally in the study of mean field control problems for multi-agent systems. We consider a multi-agent system subject to a centralized controller aiming to minimize a cost function where the microscopic dynamics of each agent is given by a differential inclusion. We model the distribution of agents by a probability measure, and formulate the minimization problem as a Mayer problem for a dynamics in the Wasserstein space represented by a controlled continuity equation describing the macroscopical evolution of the system.

Download Seminari di Equazioni Differenziali e Applicazioni