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

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.