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Numerische Mathematik

, Volume 132, Issue 2, pp 217–241 | Cite as

Well-posedness of a conservation law with non-local flux arising in traffic flow modeling

  • Sebastien BlandinEmail author
  • Paola Goatin
Article

Abstract

We prove the well-posedness of entropy weak solutions of a scalar conservation law with non-local flux arising in traffic flow modeling. The result is obtained providing accurate \(\mathbf {L^\infty }\), BV and \(\mathbf {L^1}\) estimates for the sequence of approximate solutions constructed by an adapted Lax-Friedrichs scheme.

Mathematics Subject Classification

65M12 

Notes

Acknowledgments

The authors wish to thank Rinaldo M. Colombo and Frédéric Lagoutière for useful discussions, and the anonymous reviewers for valuable suggestions that helped to improve the paper.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.IBM Research CollaboratorySingaporeSingapore
  2. 2.INRIA Sophia Antipolis - MéditerranéeSophia AntipolisFrance

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