  We consider the finite-time stabilization of homogeneous quasilinear
hyperbolic systems with one side controls and with nonlinear boundary condition
at the other side. We present time-independent feedbacks leading to the
finite-time stabilization in any time larger than the optimal time for the null
controllability of the linearized system if the initial condition is
sufficiently small. One of the key technical points is to establish the local
well-posedness of quasilinear hyperbolic systems with nonlinear, non-local
boundary conditions.
