Self-similar motions of a photon gas and the Friedmann model

The properties of self-similar motions of a gas with an equation of state p=epsilon/3 are considered. The existence of a nonsingular horizont for all solutions with a weak discontinuity is established. The Friedmann solution enters a one-parameter family of solutions which are continuous at the symmetry center. A decription of the solution is presented. Solutions with strong shock waves correspond to the problem of initial focussing of the gas toward the center in the case of a supercritical discontinuity intensity. Results of a qualitative and numerical investigation of the respective dynamic system are given. New cosmological solutions with strong and weak discontinuities are obtained