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Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications

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

  • Yves Achdou
  • Guy Barles
  • Hitoshi Ishii
  • Grigory L. Litvinov

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

Also part of the C.I.M.E. Foundation Subseries book sub series (LNMCIME, volume 2074)

About this book

Introduction

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).

Keywords

49-02, 35F21, 49L25, 35B40, 49N70, 91A13, 14T05,15A80 Hamilton Jacobi Bellman equations Large time behavior Mean field games Tropical and idempotent analysis

Authors and affiliations

  • Yves Achdou
    • 1
  • Guy Barles
    • 2
  • Hitoshi Ishii
    • 3
  • Grigory L. Litvinov
    • 4
  1. 1.UMR 7598Lab. Jacques-Louis Lions - UPMCParisFrance
  2. 2.et Physique Théorique, UMR 6083Laboratoire de MathématiquesTOURSFrance
  3. 3.Department of MathematicsWaseda UniversityShinjuku-ku, TokyoJapan
  4. 4.Institution, for Information Transmission ProblemsRusssian Academy of SciencesMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-36433-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-36432-7
  • Online ISBN 978-3-642-36433-4
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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