text: The asymptotic behavior of the central region can be investigated by taking the limit . From the figure, it can be observed that the density falls to zero very rapidly behind the shock wave. The entire mass of the gas which was initially spread out uniformly in a sphere of radius  is now contained in a thin layer behind the shock wave, that is to say, all the mass is driven outwards by the acceleration imparted by the shock wave. Thus, most of the region is basically empty. The pressure ratio also drops rapidly to attain the constant value . The temperature ratio follows from the ideal gas law; since density ratio decays to zero and the pressure ratio is constant, the temperature ratio must become infinite. The limiting form for the density is given as follows
  Remember that the density  is time-independent whereas  which means that the actual pressure is in fact time dependent. It becomes clear if the above forms are rewritten in dimensional units,
  The velocity ratio has the linear behavior in the central region,
  whereas the behavior of the velocity itself is given by