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We consider the initial boundary value problem (IBVP) for a non-local scalarconservation laws in one space dimension. The non-local operator in the fluxfunction is not a mere convolution product, but it is assumed to be aware ofboundaries. Introducing an adapted Lax-Friedrichs algorithm, we provide variousestimates on the approximate solutions that allow to prove the existence ofsolutions to the original IBVP. The uniqueness follows from the Lipschitzcontinuous dependence on initial and boundary data, which is proved exploitingresults available for the local IBVP.

Well-posedness of IBVP for 1D scalar non-local conservation laws