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Networks and Heterogeneous Media

2010, Volume 5, Issue 4: 691-709. doi: 10.3934/nhm.2010.5.691
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Classical solutions and feedback stabilization for the gas flow in a sequence of pipes

  • 1.
    Lehrstuhl 2 für Angewandte Mathematik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Martensstr. 3, 91058 Erlangen
  • Received: 01 February 2010 Revised: 01 August 2010

  • 76N25, 35L50, 93C20.

  • We consider the subcritical flow in gas networks consisting of a finite linear sequence of pipes coupled by compressor stations. Such networks are important for the transportation of natural gas over large distances to ensure sustained gas supply. We analyse the system dynamics in terms of Riemann invariants and study stationary solutions as well as classical non-stationary solutions for a given finite time interval. Furthermore, we construct feedback laws to stabilize the system locally around a given stationary state. To do so we use a Lyapunov function and prove exponential decay with respect to the L2-norm.

    Citation: Markus Dick, Martin Gugat, Günter Leugering. Classical solutions and feedback stabilization for the gas flow in a sequence of pipes[J]. Networks and Heterogeneous Media, 2010, 5(4): 691-709. doi: 10.3934/nhm.2010.5.691

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  • We consider the subcritical flow in gas networks consisting of a finite linear sequence of pipes coupled by compressor stations. Such networks are important for the transportation of natural gas over large distances to ensure sustained gas supply. We analyse the system dynamics in terms of Riemann invariants and study stationary solutions as well as classical non-stationary solutions for a given finite time interval. Furthermore, we construct feedback laws to stabilize the system locally around a given stationary state. To do so we use a Lyapunov function and prove exponential decay with respect to the L2-norm.


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    [10] M. Herty, J. Mohring and V. Sachers, A new model for gas flow in pipe networks, Math. Methods Appl. Sci., 33 (2010), 845-855.
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    [12] G. Leugering and E. J. P. G. Schmidt, On the modelling and stabilization of flows in networks of open canals, SIAM J. Control Optim., 41 (2002), 164-180. doi: 10.1137/S0363012900375664
    [13] T. Li, B. Rao and Z. Wang, Exact boundary controllability and observability for first order quasilinear hyperbolic systems with a kind of nonlocal boundary conditions, Discrete Contin. Dyn. Syst., 28 (2010), 243-257. doi: 10.3934/dcds.2010.28.243
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