  We investigate the finite-time boundary stabilization of a 1-D first order
quasilinear hyperbolic system of diagonal form on [0,1]. The dynamics of both
boundary controls are governed by a finite-time stable ODE. The solutions of
the closed-loop system issuing from small initial data in Lip([0,1]) are shown
to exist for all times and to reach the null equilibrium state in finite time.
When only one boundary feedback law is available, a finite-time stabilization
is shown to occur roughly in a twice longer time. The above feedback strategy
is then applied to the Saint-Venant system for the regulation of water flows in
a network of canals.
