Well-posedness of a conservation law with non-local flux arising in traffic flow modeling

Sebastien Blandin (1) , Paola Goatin (2)

1 IBM Research Collaboratory [Singapore]
2 ACUMES - Analysis and Control of Unsteady Models for Engineering Sciences

We prove the existence and stability of entropy weak solutions of a scalar conservation law with non-local flux arising in traffic flow modeling. The result is obtained providing accurate L\infty , BV and L1 estimates for the sequence of approximate solutions constructed by an adapted Lax-Friedrichs scheme.

Mots clés: Macroscopic Traffi c Models; Lax-Friedrichs scheme; Non-local flux; Scalar conservation laws

Domaines: Equations aux dérivées partielles [math.AP]

Sebastien Blandin, Paola Goatin. Well-posedness of a conservation law with non-local flux arising in traffic flow modeling. Numerische Mathematik, 2016, ⟨10.1007/s00211-015-0717-6⟩. ⟨hal-00954527⟩