  We report experimental and numerical results on the buildup of the energy
spectrum in wave turbulence of a vibrating thin elastic plate. Three steps are
observed: first a short linear stage, then the turbulent spectrum is
constructed by the propagation of a front in wave number space and finally a
long time saturation due to the action of dissipation. The propagation of a
front at the second step is compatible with scaling predictions from the Weak
Turbulence Theory.
