Free Access
| Issue |
ESAIM: M2AN
Volume 40, Number 5, September-October 2006
|
|
|---|---|---|
| Page(s) | 939 - 960 | |
| DOI | https://doi.org/10.1051/m2an:2006037 | |
| Published online | 16 January 2007 | |
- A. Aw and M. Rascle, Resurrection of second order models of traffic flow? SIAM J. Appl. Math. 60 (2000) 916–938. [CrossRef] [MathSciNet] [Google Scholar]
- A. Bressan, Hyperbolic Systems of Conservation Laws. Oxford University Press, Oxford (2000). [Google Scholar]
- C.M. Dafermos, Polygonal approximations of solutions of the initial value problem for a conservation law. J. Math. Anal. Appl. 38 (1972) 33–41. [CrossRef] [MathSciNet] [Google Scholar]
- K. Ehrhardt and M. Steinbach, Nonlinear optimization in gas networks, in Modeling, Simulation and Optimization of Complex Processes, H.G. Bock, E. Kostina, H.X. Phu, R. Ranacher Eds. (2005) 139–148. [Google Scholar]
- M. Gugat, Optimal nodal control of networked hyperbolic systems: Evaluation of derivatives. AMO Advanced Modeling and Optimization 7 (2005) 9–37. [Google Scholar]
- M. Gugat, G. Leugering, K. Schittkowski and E.J.P.G. Schmidt, Modelling, stabilization and control of flow in networks of open channels, in Online optimization of large scale systems, M. Grötschel, S.O. Krumke, J. Rambau Eds., Springer (2001) 251–270. [Google Scholar]
- M. Gugat, G. Leugering and E.J.P.G. Schmidt, Global controllability between steady supercritical flows in channel networks. Math. Meth. Appl. Sci. (2003) 781–802. [Google Scholar]
- M. Gugat, M. Herty, A. Klar and G. Leugering, Optimal control for traffic flow networks. J. Optim. Theory Appl. 126 (2005) 589–616. [CrossRef] [MathSciNet] [Google Scholar]
- D. Helbing, Verkehrsdynamik. Springer-Verlag, Berlin, Heidelberg, New York (1997). [Google Scholar]
- R. Holdahl, H. Holden and K.-A. Lie, Unconditionally stable splitting methods for the shallow water equations. BIT 39 (1999) 451–472. [CrossRef] [MathSciNet] [Google Scholar]
- H. Holden and L. Holden, On scalar conservation laws in one-dimension, in Ideas and Methods in Mathematical Analysis, Stochastics and Applications S. Albeverio, J. Fenstad, H. Holden, T. Lindstrøm Eds. (1992) 480–509. [Google Scholar]
- H. Holden and N.H. Risebro, A mathematical model of traffic flow on a network of unidirectional roads. SIAM J. Math. Anal. 26 (1995) 999–1017. [CrossRef] [MathSciNet] [Google Scholar]
- H. Holden and N.H. Risebro, Front tracking for hyperbolic conservation laws. Springer, New York, Berlin, Heidelberg (2002). [Google Scholar]
- H. Holden, L. Holden and R. Hoegh-Krohn, A numerical method for first order nonlinear scalar conservation laws in one-dimension. Comput. Math. Anal. 15 (1988) 595–602. [CrossRef] [Google Scholar]
- S.N. Kruzkov, First order quasi linear equations in several independent variables. Math. USSR Sbornik, 10 (1970) 217–243. [Google Scholar]
- R.J. LeVeque, Numerical methods for conservation laws. Birkhäuser Verlag, Basel, Boston, Berlin (1990). [Google Scholar]
- M.J. Lighthill and J.B. Whitham, On kinematic waves. Proc. Roy. Soc. Lond. A229 (1955) 281–345. [Google Scholar]
- J. Smoller, Shock waves and reaction diffusion equations. Springer, New York, Berlin, Heidelberg (1994). [Google Scholar]
- S. Ulbrich, A sensitivity and adjoint calculus for discontinuous solutions of hyperbolic conservation laws with source terms. SIAM J. Control Optim. 41 (2002) 740–797. [CrossRef] [MathSciNet] [Google Scholar]
- S. Ulbrich, Adjoint-based derivative computations for the optimal control of discontinuous solutions of hyperbolic conservation laws. Syst. Control Lett. 3 (2003) 309–324. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.