Mathematical Methods in the Applied Sciences

Research Article

A mixed ODE–PDE model for vehicular traffic

Corresponding Author

Rinaldo M. Colombo

Unità INdAM, Università degli Studi di Brescia, Via Branze, 38, 25123 Brescia, Italy

Correspondence to: Rinaldo M. Colombo, Unità INdAM, Università degli Studi di Brescia, Via Branze, 38, 25123 Brescia, Italy.

E-mail: [email protected]

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Francesca Marcellini,

Francesca Marcellini

Dip. di Matematica e Applicazioni, Università di Milano – Bicocca, Via Cozzi, 55, 20125 Milano, Italy

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Rinaldo M. Colombo,

Corresponding Author

Rinaldo M. Colombo

Unità INdAM, Università degli Studi di Brescia, Via Branze, 38, 25123 Brescia, Italy

Correspondence to: Rinaldo M. Colombo, Unità INdAM, Università degli Studi di Brescia, Via Branze, 38, 25123 Brescia, Italy.

E-mail: [email protected]

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Francesca Marcellini,

Francesca Marcellini

Dip. di Matematica e Applicazioni, Università di Milano – Bicocca, Via Cozzi, 55, 20125 Milano, Italy

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First published: 10 April 2014

https://doi.org/10.1002/mma.3146

Citations: 13

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Abstract

We present a traffic flow model consisting of a gluing between the Lighthill–Whitham and Richards macroscopic model with a first-order microscopic following the leader model. The basic analytical properties of this model are investigated. Existence and uniqueness are proved, as well as the basic estimates on the dependence of solutions from the initial data. Moreover, numerical integrations show some qualitative features of the model, in particular the transfer of information among regions where the different models are used. Copyright © 2014 John Wiley & Sons, Ltd.

References

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Volume38, Issue7

15 May 2015

Pages 1292-1302

A mixed ODE–PDE model for vehicular traffic

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A mixed ODE–PDE model for vehicular traffic

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