This 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.
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