PDE Models for Multi-Agent Phenomena
著者
書誌事項
PDE Models for Multi-Agent Phenomena
（Springer INdAM series / editor in chief V. Ancona, v. 28）
Springer International Publishing : Springer, c2018
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注記
Includes bibliographical references
内容説明・目次
内容説明
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.
目次
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.
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