Thresholds for shock formation in traffic flow models with nonlocal-concave-convex flux (Q1993977)
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scientific article; zbMATH DE number 6973902
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Thresholds for shock formation in traffic flow models with nonlocal-concave-convex flux |
scientific article; zbMATH DE number 6973902 |
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Thresholds for shock formation in traffic flow models with nonlocal-concave-convex flux (English)
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6 November 2018
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The author identifies sub-thresholds for finite time shock formation in a class of non-local conservation law with concavity changing flux. From a class of non-local conservation laws, the Riccati-type ODE system, that governs a solution's gradient, is obtained. The changes in concavity of the flux function correspond to the sign changes in the leading coefficient functions of the ODE system. A blow up condition of this structurally generalized Riccati-type ODE is identified. The method is illustrated via the traffic flow models with nonlocal-concave-convex flux. The techniques and ideas developed in this paper are applicable to a large class of non-local conservation laws.
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nonlocal conservation law
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traffic flow
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shock formation
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blow up
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critical threshold
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nonconcave flux
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look-ahead dynamics
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0.9329158
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