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On the Modelling and Stabilization of Flows in Networks of Open Canals

In this paper, we present a model for the controlled flow of a fluid through a network of canals using a coupled system of St. Venant equations. We then generalize in a variety of ways recent results of Coron, d'Andrea-Novel, and Bastin concerning the stabilizability around equilibrium of the flow through a single channel. This work is based on the theory of quasilinear hyperbolic systems and, in particular, on a delicate result of Li Ta-tsien concerning the existence and decay of global classical solutions.