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A fluid dynamical treatment of an ultra-relativistic spherical blast wave enclosed by a strong shock is presented. A simple similarity solution describing the explosion of a fixed amount of energy in a uniform medium is derived, and this is generalized to include cases in which power is supplied by a central source and the density of the external medium varies with radius. Radiative shocks, in which the escaping photons carry away momentum as well as energy, are also discussed. Formulas that interpolate between the non- and ultra-relativistic limits are proposed.
Blandford et al. (1976) studied this question.