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" PDE models for multi-agent phenomena / "
editors Pierre Cardaliaguet, Alessio Porretta and Francesco Salvarani.
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BL
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| Record Number
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859633
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| Title & Author
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PDE models for multi-agent phenomena /\ editors Pierre Cardaliaguet, Alessio Porretta and Francesco Salvarani.
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| Publication Statement
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Cham :: Springer,, 2018.
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| Series Statement
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Springer INdAM series ;; volume 28
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| Page. NO
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1 online resource
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| ISBN
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3030019462
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: 3030019470
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: 9783030019464
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: 9783030019471
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9783030019464
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| Bibliographies/Indexes
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Includes bibliographical references.
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| Contents
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Intro; Preface; Contents; About the Editors; Uniqueness of Solutions in Mean Field Games with Several Populations and Neumann Conditions; 1 Introduction; 2 The Uniqueness Theorem; 2.1 The Main Result; 2.2 Examples and Remarks; 3 Special Cases and Applications; 3.1 Well-Posedness of Segregation Models; 3.2 Well-Posedness of Robust Mean Field Games; Appendix: A Comparison Principle; References; Finite Difference Methods for Mean Field Games Systems; 1 Introduction; 2 A Finite Difference Scheme for Mean Field Games on the Torus; 2.1 Convergence for V Nonlocal Operator
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2.2 Convergence for V Local Operator3 Mean Field Games on Networks; 3.1 Networks and Functional Spaces; 3.2 A Formal Derivation of the MFG System on a Network; 3.3 A Finite Difference Scheme for Mean Field Games on Networks; 3.4 Existence, Uniqueness and Convergence of the Numerical Scheme; 4 A Quasi-Newton Method for Stationary Mean Field Games; 4.1 MFG in Euclidean Spaces; 4.2 Multi-Population MFG in Euclidean Spaces; 4.3 MFG on Networks; References; Existence and Uniqueness for Mean Field Games with StateConstraints; 1 Introduction; 2 Preliminaries; 2.1 Notation
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2.2 Results from Measure Theory3 Constrained MFG Equilibria; 3.1 Approximation of Constrained Trajectories; 3.2 Assumptions; 3.3 Existence of Constrained MFG Equilibria; 3.4 Proof of Theorem 3.1; 4 Mild Solution of the Constrained MFG Problem; References; An Adjoint-Based Approach for a Class of Nonlinear Fokker-Planck Equations and Related Systems; 1 Introduction; 2 Adjoint Structure; 2.1 Linearization and Duality; 2.2 Boundary Conditions; 3 Properties; 4 Numerical Approach; 4.1 Finite Differences; 4.2 Semi-Lagrangian Scheme; 5 Applications to Systems of PDEs
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5.1 Example: Hughes Model in 1-D5.2 Example: 1-D Forward-Forward Mean-Field Games; 5.3 Example: Hughes Model in 2-D; 6 Conclusions; References; Variational Mean Field Games for Market Competition; 1 Introduction; 1.1 Explanation of the Model; 1.2 Notation and Assumptions; 2 Analysis of the System; 2.1 Uniqueness Revisited for the Model of Chan and Sircar; 3 Optimal Control of Fokker-Planck Equation; 4 First-Order Case; References; A Review for an Isotropic Landau Model; 1 Introduction; 1.1 The Isotropic Landau Equation; 1.2 Conserved Quantities and Entropy Structure
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| Abstract
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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.--
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| Subject
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Computer simulation, Congresses.
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Mathematical models, Congresses.
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Computer simulation.
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Mathematical models.
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SCIENCE-- System Theory.
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TECHNOLOGY ENGINEERING-- Operations Research.
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| Dewey Classification
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003/.3
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| LC Classification
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QA76.9.C65
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| Added Entry
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Cardaliaguet, Pierre
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Porretta, Alessio
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Salvarani, Francesco
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