Level Sets of Viscosity Solutions: some Applications to Fronts and Rendez-vous Problems

The authors treat some applications of Hamilton–Jacobi equations to the study of a flame front propagation model and the rendez-vows problem. The solution of both problems requires the determination of the level sets of the viscosity solution for the corresponding equation. In the flame front propagation model described here, it is assumed that the evolution is driven by a vector field satisfying a transversality condition at time $t = 0$. The evolution in the normal direction with variable velocity $c( x ) \geq 0$ is considered as a special case. This approach is constructive, permitting the numerical solution of such problems.