76 citations · 363 across the 36 of their papers we have counts for
43 papers
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…
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…
The twin blow-up method for Hamilton-Jacobi equations in higher dimension
Nicolas Forcadel, Cyril Imbert, Regis Monneau
In this paper, we show how to extend the twin blow-up method recently developped by the authors (Comptes Rendus. Math., 2024), in order to obtain a new comparison principle for an…
A class of germs arising from homogenization in traffic flow on junctions
Pierre Cardaliaguet, Nicolas Forcadel, Regis Monneau
We consider traffic flows described by conservation laws. We study a 2:1 junction (with two incoming roads and one outgoing road) or a 1:2 junction (with one incoming road and two…
Conservation law and Hamilton-Jacobi equations on a junction: the convex case
Pierre Cardaliaguet, Nicolas Forcadel, Theo Girard +1
The goal of this paper is to study the link between the solution to an Hamilton-Jacobi (HJ) equation and the solution to a Scalar Conservation Law (SCL) on a special network. When…
Coercive Hamilton-Jacobi equations in domains: the twin blow-ups method
Nicolas Forcadel, Cyril Imbert, Regis Monneau
In this note, we consider an evolution coercive Hamilton-Jacobi equation posed in a domain and supplemented with a boundary condition. We are interested in proving a comparison pri…