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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.
The volume covers most of the topics addressed and discussed during
the Workshop INdAM "Recent advances in kinetic equations and
applications", which took place in Rome (Italy), from November 11th
to November 15th, 2019. The volume contains results on kinetic
equations for reactive and nonreactive mixtures and on collisional
and noncollisional Vlasov equations for plasmas. Some contributions
are devoted to the study of phase transition phenomena, kinetic
problems with nontrivial boundary conditions and hierarchies of
models. The book, addressed to researchers interested in the
mathematical and numerical study of kinetic equations, provides an
overview of recent advances in the field and future research
directions.
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