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math.AP2025
Beyond uniqueness: Relaxation calculus of junction conditions for coercive Hamilton-Jacobi equations
Nicolas Forcadel, Regis Monneau
A junction is a particular network given by the collection of half lines glued together at the origin. On such a junction, we consider evolutive Hamilton-Jac…
math.AP2024
Limits of non-local approximations to the Eikonal equation on manifolds
Jalal M. Fadili, Nicolas Forcadel, Rita Zantout
In this paper, we consider a non-local approximation of the time-dependent Eikonal equation defined on a Riemannian manifold. We show that the local and the non-local problems are…
math.AP2024
Germs for scalar conservation laws: the Hamilton-Jacobi equation point of view
Nicolas Forcadel, Cyril Imbert, Regis Monneau
We prove that the entropy solution to a scalar conservation law posed on the real line with a flux that is discontinuous at one point (in the space variable) coincides with the der…