Early evolution of spherical ejecta expanding into the circumstellar   matter at ultra-relativistic speeds
  We present a new self-similar solution describing early evolution of an ultra-relativistic flow resulting from a collision of homologously expanding spherical ejecta with the circumstellar matter, in which a shock wave propagates in the circumstellar matter while a weak discontinuity propagates in the ejecta at the sound speed 
Toshikazu Shigeyama, Akihiro Suzuki and Ko Nakamura
astro-ph.HE physics.flu-dyn