Well-posedness and finite volume approximations of the LWR traffic flow model with non-local velocity. (English) Zbl 1350.35117
Summary: We consider an extension of the traffic flow model proposed by Lighthill, Whitham and Richards, in which the mean velocity depends on a weighted mean of the downstream traffic density. We prove well-posedness and a regularity result for entropy weak solutions of the corresponding Cauchy problem, and use a finite volume central scheme to compute approximate solutions. We perform numerical tests to illustrate the theoretical results and to investigate the limit as the convolution kernel tends to a Dirac delta function.
MSC:
| 35L65 | Hyperbolic conservation laws |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 90B20 | Traffic problems in operations research |
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
| 35L04 | Initial-boundary value problems for first-order hyperbolic equations |
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