  In this paper we consider laser intensities larger than $10^{16} W/cm^2$
where the ablation pressure is negligible in comparison with the radiation
pressure. The radiation pressure is caused by the ponderomotive force acting
mainly on the electrons that are separated from the ions to create a double
layer (DL). This DL is accelerated into the target, like a piston that pushes
the matter in such a way that a shock wave is created. Here we discuss two
novel ideas. First is the transition domain between the relativistic and
non-relativistic laser induced shock waves. Our solution is based on
relativistic hydrodynamics also for the above transition domain. The
relativistic shock wave parameters, such as compression, pressure, shock wave
and particle flow velocities, sound velocity and rarefaction wave velocity in
the compressed target, and the temperature are calculated. Secondly, we would
like to use this transition domain for shock wave induced ultrafast ignition of
a pre-compressed target. The laser parameters for these purposes are calculated
and the main advantages of this scheme are described. If this scheme is
successful a new source of energy in large quantities may become feasible.
