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Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications

Cetraro, Italy 2011, Editors: Paola Loreti, Nicoletta Anna Tchou

  • Book
  • © 2013

Overview

Authors:
  1. Yves Achdou

    1. UMR 7598, Lab. Jacques-Louis Lions - UPMC, Paris, France

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  2. Guy Barles

    1. et Physique Théorique, UMR 6083, Laboratoire de Mathématiques, TOURS, France

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  3. Hitoshi Ishii

    1. Department of Mathematics, Waseda University, Shinjuku-ku, Tokyo, Japan

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  4. Grigory L. Litvinov

    1. Institution, for Information Transmission Problems, Russsian Academy of Sciences, Moscow, Russia

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  • It contains a quick and up to date introduction to viscosity solutions of Hamilton-Jacobi equations for graduate students or young researchers.
  • Two approaches to large time behavior of periodic solutions of Hamilton-Jacobi Equations are given: PDE and weak KAM theory.
  • Contributions on hot topics like for example numerical for mean field games should be of interest for many researchers
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2074)

Part of the book sub series: C.I.M.E. Foundation Subseries (LNMCIME)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-xv
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  2. Finite Difference Methods for Mean Field Games

    • Yves Achdou
    Pages 1-47

  3. An Introduction to the Theory of Viscosity Solutions for First-Order Hamilton–Jacobi Equations and Applications

    • Guy Barles
    Pages 49-109

  4. A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton–Jacobi Equations

    • Hitoshi Ishii
    Pages 111-249

  5. Idempotent/Tropical Analysis, the Hamilton–Jacobi and Bellman Equations

    • Grigory L. Litvinov
    Pages 251-301

  6. Back Matter

    Pages 303-304
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Keywords

About this book

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).

Authors and Affiliations

  • UMR 7598, Lab. Jacques-Louis Lions - UPMC, Paris, France

    Yves Achdou

  • et Physique Théorique, UMR 6083, Laboratoire de Mathématiques, TOURS, France

    Guy Barles

  • Department of Mathematics, Waseda University, Shinjuku-ku, Tokyo, Japan

    Hitoshi Ishii

  • Institution, for Information Transmission Problems, Russsian Academy of Sciences, Moscow, Russia

    Grigory L. Litvinov

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