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

Abstract

We prove the well-posedness of entropy weak solutions of a scalar conservation law with non-local flux arising in traffic flow modeling. The result is obtained providing accurate $$\mathbf {L^\infty }$$L∞, BV and $$\mathbf {L^1}$$L1 estimates for the sequence of approximate solutions constructed by an adapted Lax-Friedrichs scheme.