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Nonlocal reaction traffic flow model with on-off ramps (2109.04141v1)
Published 9 Sep 2021 in math.AP, cs.NA, and math.NA
Abstract: We present a non-local version of a scalar balance law modeling traffic flow with on-ramps and off-ramps. The source term is used to describe the traffic flow over the on-ramp and off-ramps. We approximate the problem using an upwind-type numerical scheme and we provide L\infty and BV estimates for the sequence of approximate solutions. Together with a discrete entropy inequality, we also show the well-posedness of the considered class of scalar balance laws. Some numerical simulations illustrate the behaviour of solutions in sample cases.