Relativistic solutions to the problem of jets with time-dependent   injection velocities
  We present a ballistic description of the propagation of the working surface of a relativistic jet. Using simple laws of conservation of mass and linear momentum at the working surface, we obtain a full description of the jet flow parametrised by the initial velocity and mass injection. This analysis will soon be applied to particular cases of time-dependent injection of mass and velocity into the jet. 
S. Mendoza, J.C. Hidalgo