3 papers
math.AP2023★ 2 cited
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…
math.AP2023
The mathematical theory of Hughes' model: a survey of results
Debora Amadori, Boris Andreianov, Marco Di Francesco +9
We provide an overview of the results on Hughes' model for pedestrian movements available in the literature. After the first successful approaches to solving a regularised version…
math.AP2023★ 1 cited
Existence of solutions to a class of one-dimensional models for pedestrian evacuations
Boris Andreianov, Theo Girard
In the framework inspired by R. L. Hughes model (Transp. Res. B, 2002) for pedestrian evacuation in a corridor, we establish existence of a solution by a topological fixed point ar…