TY  - JOUR
A1  - Gugat, Martin
A1  - Schultz, Rüdiger
A1  - Schuster, Michael
T1  - Convexity and Starshapedness of Feasible Sets in Stationary Flow Networks
T2  - Networks and Heterogeneous Media
N2  - We deal with a stationary model for flow through a
network. The flows are determined by the values at the boundary nodes of the
network that we call the loads of the network. In the applications , the feasible loads
must satisfy some box constraints. We analyze the structure of the set of feasible
loads. Our analysis is motivated by gas pipeline flows, where the box constraints are
pressure bounds.
We present sufficient conditions to show, that the feasible set is star-shaped with
respect to special points. For stronger conditions, we prove the convexity of the
set of feasible loads. All the results are given for active and passive networks, i.e.
networks with and without inner control.
This analysis is motivated by the aim to use the spheric-radial decomposition for
stochastic boundary data in this model. This paper can be used for simplifying the
algorithmic use of the spheric-radial decomposition.
KW  - Validation of nominations, Stationary states, Isothermal Euler equations, Gas networks, Convexity, Star-Shapedness, Spheric-radial decomposition
Y1  - 2019
UR  - https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/267
SP  - 171
EP  - 195
ER  -