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

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Academic year: 2021

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Fig. 1 Density profiles at t = 0.5 corresponding to a Riemann-like initial datum with ρ L = 0.6, ρ R = 0.2
Fig. 2 Density profiles at t = 0.2 corresponding to a Riemann-like initial datum with ρ L = 0.4, ρ R = 0.9
Fig. 3 Density profiles at t = 0.5 (left) and the total variation TV(ρ(t, · ); [ − 1, 1]) for t ∈ [0, 1] (right) corresponding to the Riemann-like initial datum with ρ L = 0.4, ρ R = 0.9 for w η (x) = 1/η (top), w η (x) = 2(η − x)/η 2 (middle) and w η (x)
Fig. 4 Density profiles at t = 0.5 (top) and and t = 1 (bottom) corresponding to the Riemann-like initial datum with ρ L = 0.4, ρ R = 0.9 for w η (x) = 1/η and η = 0.1,0.01, 0.001.
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