Classical solutions and feedback stabilization for the gas flow in a sequence of pipes

Markus Dick; Martin Gugat; Günter Leugering

doi:10.3934/nhm.2010.5.691

Article Contents

2010, Volume 5, Issue 4: 691-709. Doi: 10.3934/nhm.2010.5.691

This issue Previous Article Coupling conditions for the $3\times 3$ Euler system Next Article The heterogeneous multiscale finite element method for advection-diffusion problems with rapidly oscillating coefficients and large expected drift

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: January 31, 2010

Revised: July 31, 2010

Published: November 2010

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Abstract

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 $L^2$-norm.

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Mathematics Subject Classification: 76N25, 35L50, 93C20.

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