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Coupling conditions for the $3\times 3$ Euler system
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, Germany, Germany |
References:
[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. |
[2] |
M. K. Banda, M. Herty and A. Klar, Gas flow in pipeline networks, Netw. Heterog. Media, 1 (2006), 41-56. |
[3] |
J. F. Bonnans and J. André, "Optimal Structure of Gas Transmission Trunklines," Research Report available at Centre de recherche INRIA Saclay, January 7, 2009. |
[4] |
R. M. Colombo, G. Guerra, M. Herty and V. Schleper, Optimal control in networks of pipes and canals, SIAM J. Control Optim., 48 (2009), 2032-2050.
doi: 10.1137/080716372. |
[5] |
R. M. Colombo, M. Herty and V. Sachers, On 2 $\times$ 2 conservation laws at a junction, SIAM J. Math. Anal., 40 (2008), 605-622.
doi: 10.1137/070690298. |
[6] |
J.-M. Coron, B. d'Andréa-Novel and G. Bastin, A strict Lyapunov function for boundary control of hyperbolic systems of conservation laws, IEEE Trans. Automat. Control, 52 (2007), 2-11.
doi: 10.1109/TAC.2006.887903. |
[7] |
M. Gugat, Optimal nodal control of networked hyperbolic systems: Evaluation of derivatives, Adv. Model. Optim., 7 (2005), 9-37. |
[8] |
M. Gugat and M. Herty, Existence of classical solutions and feedback stabilization for the flow in gas networks, ESAIM Control Optim. Calc. Var., published online August 11, 2009. |
[9] |
M. Gugat and M. Sigalotti, Stars of vibrating strings: Switching boundary feedback stabilization, Netw. Heterog. Media, 5 (2010), 299-314.
doi: 10.3934/nhm.2010.5.299. |
[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. |
[11] |
M. Herty and V. Sachers, Adjoint calculus for optimization of gas networks, Netw. Heterog. Media, 2 (2007), 731-748. |
[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. |
[14] | |
[15] |
A. Osiadacz, "Simulation and Analysis of Gas Networks," Gulf Publishing Company, Houston, 1987. |
[16] |
A. Osiadacz and M. Chaczykowski, "Comparison of Isothermal and Non-Isothermal Transient Models," Technical Report available at Warsaw University of Technology, 1998. |
[17] |
A. Osiadacz and M. Chaczykowski, Comparison of isothermal and non-isothermal pipeline gas flow models, Chemical Engineering J., 81 (2001), 41-51.
doi: 10.1016/S1385-8947(00)00194-7. |
[18] | |
[19] |
E. Sletfjerding and J. S. Gudmundsson, Friction factor in high pressure natural gas pipelines from roughness measurements, International Gas Research Conference, Amsterdam, November 5-8, 2001. |
[20] |
M. C. Steinbach, On PDE solution in transient optimization of gas networks, J. Comput. Appl. Math., 203 (2007), 345-361.
doi: 10.1016/j.cam.2006.04.018. |
[21] |
Z. Wang, Exact controllability for nonautonomous first order quasilinear hyperbolic systems, Chin. Ann. Math. Ser. B, 27 (2006), 643-656.
doi: 10.1007/s11401-005-0520-2. |
show all references
References:
[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. |
[2] |
M. K. Banda, M. Herty and A. Klar, Gas flow in pipeline networks, Netw. Heterog. Media, 1 (2006), 41-56. |
[3] |
J. F. Bonnans and J. André, "Optimal Structure of Gas Transmission Trunklines," Research Report available at Centre de recherche INRIA Saclay, January 7, 2009. |
[4] |
R. M. Colombo, G. Guerra, M. Herty and V. Schleper, Optimal control in networks of pipes and canals, SIAM J. Control Optim., 48 (2009), 2032-2050.
doi: 10.1137/080716372. |
[5] |
R. M. Colombo, M. Herty and V. Sachers, On 2 $\times$ 2 conservation laws at a junction, SIAM J. Math. Anal., 40 (2008), 605-622.
doi: 10.1137/070690298. |
[6] |
J.-M. Coron, B. d'Andréa-Novel and G. Bastin, A strict Lyapunov function for boundary control of hyperbolic systems of conservation laws, IEEE Trans. Automat. Control, 52 (2007), 2-11.
doi: 10.1109/TAC.2006.887903. |
[7] |
M. Gugat, Optimal nodal control of networked hyperbolic systems: Evaluation of derivatives, Adv. Model. Optim., 7 (2005), 9-37. |
[8] |
M. Gugat and M. Herty, Existence of classical solutions and feedback stabilization for the flow in gas networks, ESAIM Control Optim. Calc. Var., published online August 11, 2009. |
[9] |
M. Gugat and M. Sigalotti, Stars of vibrating strings: Switching boundary feedback stabilization, Netw. Heterog. Media, 5 (2010), 299-314.
doi: 10.3934/nhm.2010.5.299. |
[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. |
[11] |
M. Herty and V. Sachers, Adjoint calculus for optimization of gas networks, Netw. Heterog. Media, 2 (2007), 731-748. |
[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. |
[14] | |
[15] |
A. Osiadacz, "Simulation and Analysis of Gas Networks," Gulf Publishing Company, Houston, 1987. |
[16] |
A. Osiadacz and M. Chaczykowski, "Comparison of Isothermal and Non-Isothermal Transient Models," Technical Report available at Warsaw University of Technology, 1998. |
[17] |
A. Osiadacz and M. Chaczykowski, Comparison of isothermal and non-isothermal pipeline gas flow models, Chemical Engineering J., 81 (2001), 41-51.
doi: 10.1016/S1385-8947(00)00194-7. |
[18] | |
[19] |
E. Sletfjerding and J. S. Gudmundsson, Friction factor in high pressure natural gas pipelines from roughness measurements, International Gas Research Conference, Amsterdam, November 5-8, 2001. |
[20] |
M. C. Steinbach, On PDE solution in transient optimization of gas networks, J. Comput. Appl. Math., 203 (2007), 345-361.
doi: 10.1016/j.cam.2006.04.018. |
[21] |
Z. Wang, Exact controllability for nonautonomous first order quasilinear hyperbolic systems, Chin. Ann. Math. Ser. B, 27 (2006), 643-656.
doi: 10.1007/s11401-005-0520-2. |
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