Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications Cetraro, Italy 2011, Editors: Paola Loreti, Nicoletta Anna Tchou - Achdou, Yves.; Barles, Guy.; Ishii, Hitoshi; Litvinov, Grigory L.; SpringerLink (Online service) (Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013)
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).
Finite Difference Methods For Mean Field Games -- An Introduction to the Theory of Viscosity Solutions for First-Order Hamilton-Jacobi Equations and Applications -- A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton-Jacobi Equations -- Idempotent/Tropical Analysis, the Hamilton-Jacobi and Bellman Equations.
Keywords: Mathematics; Functional equations; Differentiable dynamical systems; Differential equations, partial; Computer science -- Mathematics; Mathematical optimization; Mathematics; 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; Difference and Functional Equations