Existence of classical solutions and feedback stabilization for the flow in gas networks
ESAIM: Control, Optimisation and Calculus of Variations, Volume 17 (2011) no. 1, p. 28-51

We consider the flow of gas through pipelines controlled by a compressor station. Under a subsonic flow assumption we prove the existence of classical solutions for a given finite time interval. The existence result is used to construct Riemannian feedback laws and to prove a stabilization result for a coupled system of gas pipes with a compressor station. We introduce a Lyapunov function and prove exponential decay with respect to the L2-norm.

DOI : https://doi.org/10.1051/cocv/2009035
Classification:  76N25,  35L50,  93C20
Keywords: classical solution, networked hyperbolic systems, gas networks, feedback law, Lyapunov function
@article{COCV_2011__17_1_28_0,
     author = {Gugat, Martin and Herty, Micha\"el},
     title = {Existence of classical solutions and feedback stabilization for the flow in gas networks},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {17},
     number = {1},
     year = {2011},
     pages = {28-51},
     doi = {10.1051/cocv/2009035},
     mrnumber = {2775185},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2011__17_1_28_0}
}
Gugat, Martin; Herty, Michaël. Existence of classical solutions and feedback stabilization for the flow in gas networks. ESAIM: Control, Optimisation and Calculus of Variations, Volume 17 (2011) no. 1, pp. 28-51. doi : 10.1051/cocv/2009035. http://www.numdam.org/item/COCV_2011__17_1_28_0/

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