On the initial value problem for a class of discrete velocity models

  • Received: 22 October 2015 Accepted: 12 January 2016 Published: 01 February 2017
  • MSC : Primary: 35L03, 35Q91; Secondary: 90B20

  • In this paper we investigate the initial value problem for a class of hyperbolic systems relating the mathematical modeling of a class of complex phenomena, with emphasis on vehicular traffic flow. Existence and uniqueness for large times of solutions, a basic requisite both for models building and for their numerical implementation, are obtained under weak hypotheses on the terms modeling the interaction among agents. The results are then compared with the existing literature on the subject.

    Citation: Davide Bellandi. On the initial value problem for a class of discrete velocity models[J]. Mathematical Biosciences and Engineering, 2017, 14(1): 31-43. doi: 10.3934/mbe.2017003

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  • In this paper we investigate the initial value problem for a class of hyperbolic systems relating the mathematical modeling of a class of complex phenomena, with emphasis on vehicular traffic flow. Existence and uniqueness for large times of solutions, a basic requisite both for models building and for their numerical implementation, are obtained under weak hypotheses on the terms modeling the interaction among agents. The results are then compared with the existing literature on the subject.


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    [1] [ G. Ajmone Marsan,N. Bellomo,A. Tosin, null, Complex Systems and Society: Modeling and Simulation, Springer, 2013.
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    [12] [ V. Coscia,L. Fermo,N. Bellomo, On the mathematical theory of living systems Ⅱ: The interplay between mathematics and system biology, Comput. Math. Appl., 62 (2011): 3902-3911.
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