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
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR7351
3 Acumes - Analysis and Control of Unsteady Models for Engineering Sciences
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : 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.
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Florent Berthelin, Paola Goatin. Regularity results for the solutions of a non-local model of traffic. Discrete and Continuous Dynamical Systems - Series A, American Institute of Mathematical Sciences, In press. ⟨hal-01813760⟩

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