 A. Aw and M. Rascle, Resurrection of second order models of traffic flow? SIAM J. Appl. Math. 60 (2000) 916–938. [CrossRef] [MathSciNet]
 A. Bressan, Hyperbolic Systems of Conservation Laws. Oxford University Press, Oxford (2000).
 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]
 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.
 M. Gugat, Optimal nodal control of networked hyperbolic systems: Evaluation of derivatives. AMO Advanced Modeling and Optimization 7 (2005) 9–37.
 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.
 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.
 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]
 D. Helbing, Verkehrsdynamik. SpringerVerlag, Berlin, Heidelberg, New York (1997).
 R. Holdahl, H. Holden and K.A. Lie, Unconditionally stable splitting methods for the shallow water equations. BIT 39 (1999) 451–472. [CrossRef] [MathSciNet]
 H. Holden and L. Holden, On scalar conservation laws in onedimension, in Ideas and Methods in Mathematical Analysis, Stochastics and Applications S. Albeverio, J. Fenstad, H. Holden, T. Lindstrøm Eds. (1992) 480–509.
 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]
 H. Holden and N.H. Risebro, Front tracking for hyperbolic conservation laws. Springer, New York, Berlin, Heidelberg (2002).
 H. Holden, L. Holden and R. HoeghKrohn, A numerical method for first order nonlinear scalar conservation laws in onedimension. Comput. Math. Anal. 15 (1988) 595–602. [CrossRef]
 S.N. Kruzkov, First order quasi linear equations in several independent variables. Math. USSR Sbornik, 10 (1970) 217–243.
 R.J. LeVeque, Numerical methods for conservation laws. Birkhäuser Verlag, Basel, Boston, Berlin (1990).
 M.J. Lighthill and J.B. Whitham, On kinematic waves. Proc. Roy. Soc. Lond. A229 (1955) 281–345.
 J. Smoller, Shock waves and reaction diffusion equations. Springer, New York, Berlin, Heidelberg (1994).
 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]
 S. Ulbrich, Adjointbased derivative computations for the optimal control of discontinuous solutions of hyperbolic conservation laws. Syst. Control Lett. 3 (2003) 309–324. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed]
Free access
Issue 
ESAIM: M2AN
Volume 40, Number 5, SeptemberOctober 2006



Page(s)  939  960  
DOI  http://dx.doi.org/10.1051/m2an:2006037  
Published online  16 January 2007 