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Networks and Heterogeneous Media

2016, Volume 11, Issue 1: 107-121. doi: 10.3934/nhm.2016.11.107
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Well-posedness and finite volume approximations of the LWR traffic flow model with non-local velocity

  • 1.
    INRIA Sophia Antipolis - Méditerranée, EPI OPALE, 2004, route des Lucioles - BP 93, 06902 Sophia Antipolis Cedex
  • 2.
    Inria Sophia Antipolis - Méditerranée, 2004, route des Lucioles - BP 93, 06902 Sophia Antipolis Cedex
  • Received: 01 April 2015 Revised: 01 October 2015

  • Primary: 35L65; Secondary: 65M12, 90B20.

  • 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.

    Citation: Paola Goatin, Sheila Scialanga. Well-posedness and finite volume approximations of the LWR traffic flow model with non-local velocity[J]. Networks and Heterogeneous Media, 2016, 11(1): 107-121. doi: 10.3934/nhm.2016.11.107

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  • 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.


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