Skip to main content

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
Cancel
×
×
Home
  • Home
Article
  • Cited by 17
  • Cited by
    Crossref Citations
    Crossref logo
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Di Francesco, M. Fagioli, S. Rosini, M. D. and Russo, G. 2017. Active Particles, Volume 1. p. 333.
    Goatin, Paola and Monache, Maria Laura Delle 2017. Stability estimates for scalar conservation laws with moving flux constraints. Networks and Heterogeneous Media, Vol. 12, Issue. 2, p. 245.
    Colombo, Rinaldo M. and Holden, Helge 2016. On the Braess Paradox with Nonlinear Dynamics and Control Theory. Journal of Optimization Theory and Applications, Vol. 168, Issue. 1, p. 216.
    Göttlich, Simone and Harter, Camill 2016. A weakly coupled model of differential equations for thief tracking. Networks and Heterogeneous Media, Vol. 11, Issue. 3, p. 447.
    Bressan, Alberto and Nguyen, Khai T. 2015. Optima and equilibria for traffic flow on networks with backward propagating queues. Networks and Heterogeneous Media, Vol. 10, Issue. 4, p. 717.
    Colombo, Rinaldo M. and Marcellini, Francesca 2015. A mixed ODE-PDE model for vehicular traffic. Mathematical Methods in the Applied Sciences, Vol. 38, Issue. 7, p. 1292.
    Di Francesco, M. and Rosini, M.D. 2015. Rigorous Derivation of Nonlinear Scalar Conservation Laws from Follow-the-Leader Type Models via Many Particle Limit. Archive for Rational Mechanics and Analysis, Vol. 217, Issue. 3, p. 831.
    Marcellini, Francesca 2014. Free-congested and micro-macro descriptions of traffic flow. Discrete and Continuous Dynamical Systems - Series S, Vol. 7, Issue. 3, p. 543.
    Rossi, Elena 2014. A justification of a LWR model based on a follow the leader description. Discrete and Continuous Dynamical Systems - Series S, Vol. 7, Issue. 3, p. 579.
    Delle Monache, M.L. and Goatin, P. 2014. Scalar conservation laws with moving constraints arising in traffic flow modeling: An existence result. Journal of Differential Equations, Vol. 257, Issue. 11, p. 4015.
    Monache, Maria Laura Delle and Goatin, Paola 2014. A front tracking method for a strongly coupled PDE-ODE system with moving density constraints in traffic flow. Discrete and Continuous Dynamical Systems - Series S, Vol. 7, Issue. 3, p. 435.
    Work, Daniel B. and Tossavainen, Olli-Pekka 2013. Markov Chain Monte Carlo based inverse modeling of traffic flows using GPS data. Networks and Heterogeneous Media, Vol. 8, Issue. 3, p. 803.
    Leger, Nicholas 2011. L 2 Stability Estimates for Shock Solutions of Scalar Conservation Laws Using the Relative Entropy Method. Archive for Rational Mechanics and Analysis, Vol. 199, Issue. 3, p. 761.
    Lattanzio, Corrado Maurizi, Amelio and Piccoli, Benedetto 2011. Moving Bottlenecks in Car Traffic Flow: A PDE-ODE Coupled Model. SIAM Journal on Mathematical Analysis, Vol. 43, Issue. 1, p. 50.
    Colombo, Rinaldo M. Marcellini, Francesca and Rascle, Michel 2010. A 2-Phase Traffic Model Based on a Speed Bound. SIAM Journal on Applied Mathematics, Vol. 70, Issue. 7, p. 2652.
    Bretti, Gabriella and Piccoli, Benedetto 2008. A Tracking Algorithm for Car Paths on Road Networks. SIAM Journal on Applied Dynamical Systems, Vol. 7, Issue. 2, p. 510.
    Cortes, Jorge 2008. Discontinuous dynamical systems. IEEE Control Systems Magazine, Vol. 28, Issue. 3, p. 36.
    ×
  • Get access
    Add to cart USD35.00
    Check if you have access via personal or institutional login
    Log in Register Recommend to librarian

A Hölder continuous ODE related to traffic flow

  • Rinaldo M. Colombo (a1) and Andrea Marson (a2)
Abstract

This paper is devoted to the proof of the well posedness of a class of ordinary differential equations (ODEs). The vector field depends on the solution to a scalar conservation law. Forward uniqueness of Filippov solutions is obtained, as well as their Hölder continuous dependence on the initial data of the ODE. Furthermore, we prove the continuous dependence in C0 of the solution to the ODE from the initial data of the conservation law in L1.

This problem is motivated by a model of traffic flow.

Copyright
COPYRIGHT: © Royal Society of Edinburgh 2003
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

CAPTCHA *

Skip to the audio challenge
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 40 *
Loading metrics...

Abstract views

Total abstract views: 135 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 12th June 2018. This data will be updated every 24 hours.

Cancel
Confirm
×