Gas Flow in Fan-Shaped Networks: Classical Solutions and Feedback Stabilization

Authors:
Martin Gugat;Markus Dick;Günter Leugering
Affiliations:
gugat@am.uni-erlangen.de and dick@am.uni-erlangen.de and leugering@am.uni-erlangen.de;-;-
Venue:
SIAM Journal on Control and Optimization
Year:
2011

Citing 5
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Abstract

We analyze the subcritical gas flow through fan-shaped networks of pipes, that is, through tree-shaped networks with exactly one node where more than two pipes meet. The gas flow in pipe networks is modeled by the isothermal Euler equations, a hyperbolic PDE system of balance laws. For this system we analyze stationary states and classical nonstationary solutions locally around a stationary state on a finite time interval. Furthermore, we present a Lyapunov function and boundary feedback laws to stabilize a fan-shaped network around a given stationary state.