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We study a 1D scalar conservation law whose non-local flux has a singlespatial discontinuity. This model is intended to describe traffic flow on aroad with rough conditions. We approximate the problem through an upwind-typenumerical scheme and provide compactness estimates for the sequence ofapproximate solutions. Then, we prove the existence and the uniqueness ofentropy weak solutions. Numerical simulations corroborate the theoreticalresults and the limit model as the kernel support tends to zero is numericallyinvestigated.

Existence of entropy weak solutions for 1D non-local traffic models with space-discontinuous flux