| Issue |
ESAIM: COCV
Volume 17, Number 1, January-March 2011
|
|
|---|---|---|
| Page(s) | 28 - 51 | |
| DOI | https://doi.org/10.1051/cocv/2009035 | |
| Published online | 11 August 2009 | |
Existence of classical solutions and feedback stabilization for the flow in gas networks
1
Lehrstuhl 2 für Angewandte Mathematik, Martensstr. 3, 91058 Erlangen,
Germany. gugat@am.uni-erlangen.de
2
RWTH Aachen, Lehrstuhl C für Mathematik, Templergraben 55, 52065 Aachen,
Germany. herty@mathc.rwth-aachen.de
Received:
9
March
2009
Revised:
11
June
2009
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.
Mathematics Subject Classification: 76N25 / 35L50 / 93C20
Key words: Classical solution / networked hyperbolic systems / gas networks / feedback law / Lyapunov function
© EDP Sciences, SMAI, 2009
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