Jean-David Benamou, Philippe Hoch (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
Similarity:
We describe both the classical Lagrangian and the Eulerian methods for first order Hamilton–Jacobi equations of geometric optic type. We then explain the basic structure of the software and how new solvers/models can be added to it. A selection of numerical examples are presented.
Cyril Imbert, Régis Monneau, Hasnaa Zidani (2013)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
This paper is concerned with the study of a model case of first order Hamilton-Jacobi equations posed on a “junction”, that is to say the union of a finite number of half-lines with a unique common point. The main result is a comparison principle. We also prove existence and stability of solutions. The two challenging difficulties are the singular geometry of the domain and the discontinuity of the Hamiltonian. As far as discontinuous Hamiltonians are concerned, these results seem to...