https://hal.inria.fr/hal-00916055Falcone, MaurizioMaurizioFalconeUniversità degli Studi di Roma "La Sapienza" = Sapienza University [Rome]Ferretti, RobertoRobertoFerrettiDipartimento di Matematica [Roma TRE] - Università degli Studi Roma TreSemi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi EquationsHAL CCSD2014[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Bouzat, EstelleSensitivity Analysis for Deterministic Controller Design - SADCO - - EC:FP7:PEOPLE2011-01-01 - 2014-12-31 - 264735 - VALID - 2013-12-09 16:42:532021-11-03 14:18:072013-12-09 16:42:53enBooks1This largely self-contained book provides a unified framework of semi-Lagrangian strategy for the approximation of hyperbolic PDEs, with a special focus on Hamilton-Jacobi equations. The authors provide a rigorous discussion of the theory of viscosity solutions and the concepts underlying the construction and analysis of difference schemes; they then proceed to high-order semi-Lagrangian schemes and their applications to problems in fluid dynamics, front propagation, optimal control, and image processing. The developments covered in the text and the references come from a wide range of literature.