Regularity results for the solutions of a non-local model of traffic

Florent Berthelin (1, 2) , Paola Goatin (3, 2)

1 COFFEE - COmplex Flows For Energy and Environment
2 LJAD - Laboratoire Jean Alexandre Dieudonné
3 ACUMES - Analysis and Control of Unsteady Models for Engineering Sciences

We consider a non-local traffic model involving a convolution product. Unlike other studies, the considered kernel is discontinuous on R. We prove Sobolev estimates and prove the convergence of approximate solutions solving a viscous and regularized non-local equation. It leads to weak, $C([0,T],L^2(\R))$, and smooth, $W^{2,2N}([0,T]\times\R)$, solutions for the non-local traffic model.

Mots clés: Scalar conservation laws; Anisotropic non-local flux; Viscous; Traffic flow models

Domaines: Equations aux dérivées partielles [math.AP]

Florent Berthelin, Paola Goatin. Regularity results for the solutions of a non-local model of traffic. Discrete and Continuous Dynamical Systems - Series A, 2019, 39 (6), pp.3197-3213. ⟨hal-01813760⟩