Congested traffic dynamics , weak flows and very degenerate elliptic equations

@inproceedings{Brasco2009CongestedTD,
  title={Congested traffic dynamics , weak flows and very degenerate elliptic equations},
  author={Lorenzo Brasco and Guillaume Carlier and Filippo Santambrogio},
  year={2009}
}
Starting from a model of traffic congestion, we introduce a minimal-flow–like variational problem whose solution is characterized by a very degenerate elliptic PDE. We precisely investigate the relations between these two problems, which can be done by considering some weak notion of flow for a related ODE. We also prove regularity results for the degenerate elliptic PDE, which enables us in some cases to apply the DiPerna-Lions theory. 

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References

Publications referenced by this paper.
Showing 1-10 of 27 references

Existence

  • L. Ambrosio, G. Crippa
  • uniqueness, stability and differentiability…
  • 2008
Highly Influential
4 Excerpts

Santambrogio , A variational model for urban planning with traffic congestion

  • F. G. Carlier
  • SIAM J . Control Optim .
  • 2008

Notes on the p-Laplace equation

  • P. Lindqvist
  • Report, University of Jyväskylä Department of…
  • 2006
1 Excerpt

Transport equation and Cauchy problem for BV vector fields

  • L. Ambrosio
  • Invent. Math. 158
  • 2004
1 Excerpt

Topics in optimal transportation

  • C. Villani
  • Graduate Studies in Mathematics, 58, American…
  • 2003
1 Excerpt

Wardrop , Some theoretical aspects of road traffic research

  • G. J.
  • Proc . Inst . Civ . Eng .
  • 2003

Convex analysis and variational problems

  • I. Ekeland, R. Temam
  • Classics in Applied Mathematics, 28. SIAM…
  • 1999
1 Excerpt

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