C.I.M.E. Foundation Subseries

Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications

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

Authors: Achdou, Y., Barles, G., Ishii, H., Litvinov, G.L.

Editors: Loreti, Paola, Tchou, Nicoletta (Eds.)

  • 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
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  • ISBN 978-3-642-36433-4
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  • ISBN 978-3-642-36432-7
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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).

Table of contents (4 chapters)

  • Finite Difference Methods for Mean Field Games

    Achdou, Yves

    Pages 1-47

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

    Barles, Guy

    Pages 49-109

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

    Ishii, Hitoshi

    Pages 111-249

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

    Litvinov, Grigory L.

    Pages 251-301

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-642-36433-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-3-642-36432-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications
Book Subtitle
Cetraro, Italy 2011, Editors: Paola Loreti, Nicoletta Anna Tchou
Authors
Editors
  • Paola Loreti
  • Nicoletta Tchou
Series Title
C.I.M.E. Foundation Subseries
Series Volume
2074
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-36433-4
DOI
10.1007/978-3-642-36433-4
Softcover ISBN
978-3-642-36432-7
Edition Number
1
Number of Pages
XV, 301
Number of Illustrations and Tables
9 b/w illustrations, 2 illustrations in colour
Topics