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Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications: Cetraro, Italy 2011, Editors: Paola Loreti, Nicoletta Anna Tchou

✍ Scribed by Yves Achdou, Guy Barles, Hitoshi Ishii, Grigory L. Litvinov (auth.)

Publisher
Springer-Verlag Berlin Heidelberg
Year
2013
Tongue
English
Leaves
316
Series
Lecture Notes in Mathematics 2074
Edition
1
Category
Library
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✦ Synopsis

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).

✦ Table of Contents

Front Matter....Pages i-xv
Finite Difference Methods for Mean Field Games....Pages 1-47
An Introduction to the Theory of Viscosity Solutions for First-Order Hamilton–Jacobi Equations and Applications....Pages 49-109
A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton–Jacobi Equations....Pages 111-249
Idempotent/Tropical Analysis, the Hamilton–Jacobi and Bellman Equations....Pages 251-301
Back Matter....Pages 303-304

✦ Subjects

Calculus of Variations and Optimal Control; Optimization; Partial Differential Equations; Computational Mathematics and Numerical Analysis; Game Theory, Economics, Social and Behav. Sciences; Dynamical Systems and Ergodic Theory; Differe

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