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 L 2-norm.

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.

We consider the problem of exactly controlling the states of the de St. Venant equations from a given constant state to another constant state by applying nonlinear boundary controls. During this transition the solution stays in the class of C^1 -solutions. There are no restrictions on the distance between the initial state and the target state, so our result is a global controllability result for a nonlinear hyberbolic system. Résumé: On s’intéresse ici à un système décrit par les equations de St. Venant. On montre qu’on peut contrôler le système d’un état initial constant à un autre état constant avec des contrôles frontières non linéaires de façon qu’il y ait une solution C^1 . Il n’y a pas de restriction concernant la distance entre les données initiales et les données finales, donc notre résultat est un résultat de contrôlabilité globale exacte pour un système hyperbolique non linéaire.

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.