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.

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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