Those Lecture Notes comprise the fabric relative to the classes given on the CIME summer time college held in Cetraro, Italy from August 29 to September three, 2011. the subject was once "Hamilton-Jacobi Equations: Approximations, Numerical research and Applications". The classes dealt normally with the subsequent matters: first order and moment order Hamilton-Jacobi-Bellman equations, houses of viscosity options, asymptotic behaviors, suggest box video games, approximation and numerical tools, idempotent research. The content material of the classes ranged from an creation to viscosity strategies to particularly complicated themes, on the leading edge of study within the box. We think that they opened views on new and gentle matters. those lecture notes comprise 4 contributions via Yves Achdou (Finite distinction equipment for suggest box Games), man Barles (An advent to the speculation of Viscosity strategies for First-order Hamilton-Jacobi Equations and Applications), Hitoshi Ishii (A brief advent to Viscosity ideas and the big Time habit of strategies of Hamilton-Jacobi Equations) and Grigory Litvinov (Idempotent/Tropical research, the Hamilton-Jacobi and Bellman Equations).

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