Chapter 1: Models and motivations
Society for Industrial and Applied Mathematics eBooks · 2013
This book is devoted to the study of some class of hyperbolic PDEs and to their approximation of Semi-Lagrangian type. Throughout the book, we will try to keep a mathematically rigorous analysis as much as possible; however, before getting into the most technical details and results, we would like to start by presenting some examples and applications which have motivated much of the research in this area. In fact, the analysis and approximation of first-order PDEs of Hamilton–Jacobi (HJ) type has been driven by their application to fields such as Fluid Dynamics, optimal control and differential games, image processing, and material science just to mention the main ones.