This volume covers selected topics addressed and discussed during the workshop "PDE models for multi-agent phenomena," which was held in Rome, Italy, from November 28th to December 2nd, 2016. The content mainly focuses on kinetic equations and mean field games, which provide a solid framework for the description of multi-agent phenomena. The book includes original contributions on the theoretical and numerical study of the MFG system: the uniqueness issue and finite difference methods for the MFG system, MFG with state constraints, and application of MFG to market competition. The book also presents new contributions on the analysis and numerical approximation of the Fokker-Planck-Kolmogorov equations, the isotropic Landau model, the dynamical approach to the quantization problem and the asymptotic methods for fully nonlinear elliptic equations. Chiefly intended for researchers interested in the mathematical modeling of collective phenomena, the book provides an essential overview of recent advances in the field and outlines future research directions.

Autorentext

Pierre Cardaliaguet completed his PhD at the U. Paris Dauphine in 1994. He has been a Professor at Brest U. from 2000 to 2010 and is currently Professor at the U. Paris Dauphine.

Alessio Porretta received his PhD from the University of Rome La Sapienza in 2000, and is currently a full Professor of Mathematical Analysis at the University of Rome Tor Vergata. His research activities are mainly focused on convection-diffusion and Hamilton-Jacobi equations, control theory and mean field games.

Francesco Salvarani (PhD in Mathematics, University of Genoa, Italy, and Ecole Normale Supérieure de Cachan, France) is an expert in the mathematical and numerical study of collective phenomena arising both in physics and the social sciences. His scientific activities are mainly focused on kinetic equations and systems.

Inhalt
1 Martino Bardi and Marco Cirant, Uniqueness of solutions in Mean Field Games with several populations and Neumann conditions.- 2 Simone Cacace and Fabio Camilli, Finite difference methods for Mean Field Games systems.- 3 Piermarco Cannarsa and Rossana Capuani, Existence and uniqueness for Mean Field Games with state constraints.- 4 Adriano Festa, Diogo A. Gomes and Roberto M. Velho, An adjoint-based approach for a class of nonlinear Fokker-Planck equations and related systems.- 5 P. Jameson Graber and Charafeddine Mouzouni, Variational mean field games for market competition.- 6 Maria Gualdani and Nicola Zamponi, A review for an isotropic Landau model.- 7 Mikaela Iacobelli, A gradient flow perspective on the quantization problem.- 8 Edgard A. Pimentel and Makson S. Santos, Asymptotic methods in regularity theory for nonlinear elliptic equations: a survey.- 9 Elisabetta Carlini and Francisco J. Silva, A fully-discrete scheme for systems of nonlinear Fokker-Planck-Kolmogorov equations.