Advanced Search
Article Contents
Article Contents

Coupling conditions for the $3\times 3$ Euler system

Abstract Related Papers Cited by
  • This paper is devoted to the extension to the full $3\times3$ Euler system of the basic analytical properties of the equations governing a fluid flowing in a duct with varying section. First, we consider the Cauchy problem for a pipeline consisting of 2 ducts joined at a junction. Then, this result is extended to more complex pipes. A key assumption in these theorems is the boundedness of the total variation of the pipe's section. We provide explicit examples to show that this bound is necessary.
    Mathematics Subject Classification: Primary: 35L65; secondary: 76N10.


    \begin{equation} \\ \end{equation}
  • [1]

    M. K. Banda, M. Herty and A. Klar, Coupling conditions for gas networks governed by the isothermal Euler equations, Netw. Heterog. Media, 1 (2006), 295-314 (electronic).


    M. K. Banda, M. Herty and A. Klar, Gas flow in pipeline networks, Netw. Heterog. Media, 1 (2006), 41-56 (electronic).


    A. Bressan, "Hyperbolic Systems of Conservation Laws. The One-Dimensional Cauchy Problem," Oxford Lecture Series in Mathematics and its Applications 20, Oxford University Press, Oxford, 2000.


    R. M. Colombo and M. Garavello, On the $p$-system at a junction, in "Control Methods in Pde-Dynamical Systems," volume 426 of Contemp. Math., Amer. Math. Soc., Providence, RI, (2007), 193-217.


    R. M. Colombo and M. Garavello, On the 1D modeling of fluid flowing through a junction, preprint, (2009).


    R. M. Colombo and G. Guerra, On general balance laws with boundary, J. Diff. Equations, 248 (2010), 1017-1043.doi: 10.1016/j.jde.2009.12.002.


    R. M. Colombo, G. Guerra, M. Herty and V. Schleper, Modeling and optimal control of networks of pipes and canals, SIAM J. Math. Anal., 48 (2009), 2032-2050.


    R. M. Colombo, M. Herty and V. Sachers, On $2\times2$ conservation laws at a junction, SIAM J. Math. Anal., 40 (2008), 605-622.doi: 10.1137/070690298.


    R. M. Colombo and F. Marcellini, Smooth and discontinuous junctions in the p-system, J. Math. Anal. Appl., 361 (2010), 440-456.doi: 10.1016/j.jmaa.2009.07.022.


    R. M. Colombo and C. Mauri, Euler system at a junction, Journal of Hyperbolic Differential Equations, 5 (2008), 547-568.doi: 10.1142/S0219891608001593.


    M. Garavello and B. Piccoli, "Traffic Flow on Networks. Conservation Laws Models," AIMS Series on Applied Mathematics 1, American Institute of Mathematical Sciences (AIMS), Springfield, MO, 2006.


    P. Goatin and P. G. LeFloch, The Riemann problem for a class of resonant hyperbolic systems of balance laws, Ann. Inst. H. Poincaré Anal. Non Linéaire, 21 (2004), 881-902.doi: 10.1016/j.anihpc.2004.02.002.


    G. Guerra, F. Marcellini and V. Schleper, Balance laws with integrable unbounded source, SIAM J. Math. Anal., 41 (2009), 1164-1189.doi: 10.1137/080735436.


    H. Holden and N. H. Risebro, Riemann problems with a kink, SIAM J. Math. Anal., 30 (1999), 497-515 (electronic).doi: 10.1137/S0036141097327033.


    T. P. Liu, Nonlinear stability and instability of transonic flows through a nozzle, Comm. Math. Phys., 83 (1982), 243-260.doi: 10.1007/BF01976043.


    J. Smoller, "Shock Waves and Reaction-Diffusion Equations," Second edition, Springer-Verlag, New York, 1994.


    G. B. Whitham, "Linear and Nonlinear Waves," John Wiley & Sons Inc., New York, 1999, reprint of the 1974 original, A Wiley-Interscience Publication.

  • 加载中

Article Metrics

HTML views() PDF downloads(67) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint