PDE Models for Multi-Agent Phenomena

  • Pierre Cardaliaguet
  • Alessio Porretta
  • Francesco Salvarani

Part of the Springer INdAM Series book series (SINDAMS, volume 28)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Simone Cacace, Fabio Camilli
    Pages 21-47
  3. Piermarco Cannarsa, Rossana Capuani
    Pages 49-71
  4. Philip Jameson Graber, Charafeddine Mouzouni
    Pages 93-114
  5. Maria Gualdani, Nicola Zamponi
    Pages 115-144

About this book


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.


Partial differential equations Mean Field Games Multi-agent phenomena Kinetic system Multi-scale systems

Editors and affiliations

  • Pierre Cardaliaguet
    • 1
  • Alessio Porretta
    • 2
  • Francesco Salvarani
    • 3
  1. 1.CeremadeUniversité Paris-DauphineParisFrance
  2. 2.Dept. of MathematicsUniversitá di Roma “Tor Vergata”RomaItaly
  3. 3.Dept. of Mathematics “F. Casorati”University of PaviaPaviaItaly

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