Regularizing effect for unbounded flux-limited viscosity solutions of a discontinuous Hamilton-Jacobi equation on junction

Nader El Khatib (1) , Nicolas Forcadel (2) , Mamdouh Zaydan (1)

1 LAU - Lebanese American University
2 LMI - Laboratoire de Mathématiques de l'INSA de Rouen Normandie

In this paper, we provide regularizing effects for continuous bounded from below viscosity solutions of a discontinuous Hamilton-Jacobi equation posed on a junction. We consider different quasi-convex and coercive time-space Hamiltonians on each branch and a flux limiter condition at the junction point. We then prove that the derivative with respect to time of the solution is bounded. As consequence, we deduce that the solution of the equation is locally Lipschitz continuous.

Mots clés: AMS Classification: 35F21; 35D35; 35D40 Regularizing effects; viscosity solutions; discontinuous Hamilton-Jacobi on a junction

Domaines: Mathématiques [math]

Nader El Khatib, Nicolas Forcadel, Mamdouh Zaydan. Regularizing effect for unbounded flux-limited viscosity solutions of a discontinuous Hamilton-Jacobi equation on junction. Advances in Differential Equations, 2024, 29 (7-8), pp.477-514. ⟨hal-03721696v2⟩