# On Single-Pass Methods for Stationary Hamilton-Jacobi Equations

Simone Cacace, Emiliano Cristiani^{*} and Maurizio Falcone

The use of single-pass methods (like, e.g., the Fast Marching method) has become popular in the solution of some nonlinear hyperbolic PDEs. The prototype of these equations is the eikonal equation, where the methods can be applied saving CPU time and possibly memory allocation. Then, some natural questions arise: can single-pass methods solve any Hamilton-Jacobi equation? If not, where the limit should be set? This talk tries to give an answer to those questions.

Mathematics Subject Classification: 65N12 49L20 49M99

Keywords: Fast Marching methods; Fast Sweeping methods; eikonal equation;

Minisymposion: Dynamic Programming Approach to Optimal Control Methods and Applications