Dynamical model of an expanding shell

Expanding blast waves are ubiquitous in many astronomical sources, such as supernova remnants, X-ray emitting binaries, and gamma-ray bursts. I consider here the dynamics of such an expanding blast wave, both in the adiabatic and the radiative regimes. As the blast wave collects material from its surroundings, it decelerates. A full description of the temporal evolution of the blast wave requires consideration of both the energy density and the pressure of the shocked material. The obtained equation is different from earlier works in which only the energy was considered. The solution converges to the familiar results in both the ultrarelativistic and the sub-relativistic (Newtonian) regimes.