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- Author: Yves Achdou
- Pages: 296
- Language: English
- ISBN/ASIN: 3642364322
- ISBN13: 9783642364327
- Upload date: 15-06-2017, 20:28
- Category: Mathematics

These Lecture Notes contain the material relative to the courses given at the CIME summer school held in Cetraro, Italy from August 29 to September 3, 2011. The topic was "Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications". The courses dealt mostly with the following subjects: first order and second order Hamilton-Jacobi-Bellman equations, properties of viscosity solutions, asymptotic behaviors, mean field games, approximation and numerical methods, idempotent analysis. The content of the courses ranged from an introduction to viscosity solutions to quite advanced topics, at the cutting edge of research in the field. We believe that they opened perspectives on new and delicate issues. These lecture notes contain four contributions by Yves Achdou (Finite Difference Methods for Mean Field Games), Guy Barles (An Introduction to the Theory of Viscosity Solutions for First-order Hamilton-Jacobi Equations and Applications), Hitoshi Ishii (A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton-Jacobi Equations) and Grigory Litvinov (Idempotent/Tropical Analysis, the Hamilton-Jacobi and Bellman Equations).

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Time-Dependent Problems and Difference Methods Theoretical Numerical Analysis: A Functional Analysis Framework (Texts in Applied Mathematics) Stochastic Control Theory: Dynamic Programming Principle Recent Advances in Delay Differential and Difference Equations (Springer Proceedings in Mathematics & Statistics) Numerical Methods for Viscosity Solutions and Applications Numerical Approximation Methods: 355/113 Introduction to Computation and Modeling for Differential Equations Dynamical Systems: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 19-26, 2000 (Lecture Notes in Mathematics / C.I.M.E. Foundation Subseries) Difference Equations: Theory, Applications and Advanced Topics, Third Edition (Monographs and Research Notes in Mathematics) Difference Equations, Second Edition: An Introduction with Applications Classical and Modern Numerical Analysis: Theory, Methods and Practice (Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series) Beginning Partial Differential Equations (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts) Asymptotic Integration of Differential and Difference Equations (Lecture Notes in Mathematics) Approximate Solutions of Operator Equations Analysis of Numerical Methods (Dover Books on Mathematics) An Introduction to Numerical Methods and Analysis Advances in Computational Mathematics (Lecture Notes in Pure and Applied Mathematics) Analysis, Geometry, and Modeling in Finance: Advanced Methods in Option Pricing (Chapman & Hall/CRC Financial Mathematics Series)