Shock waves driven by the release of energy at the center of a cold ideal gas sphere of initial density rho∝ r⁻ᵒᵐᵉᵍᵃ approach a self-similar (SLS) behavior, with velocity Ṙ∝ R^delta, as R->∞. For omega>3 the solutions are of the second-type, i.e., delta is determined by the requirement that the flow should include a sonic point. No solution satisfying this requirement exists, however, in the 3≤ omega≤ omegag(gamma) ``gap'' (ωg=3.26 for adiabatic index gamma=5/3). We argue that second-type solutions should not be required in general to include a sonic point. Rather, it is sufficient to require the existence of a characteristic line r_c(t), such that the energy in the region r_c(t) ∞, and an asymptotic solution given by the SLS solution at r_c(t) omega_g and the latter identifies delta=0 solutions as the asymptotic solutions for 3≤ omega≤ omegag (as suggested by Gruzinov03). In these solutions, r_c is a C_0 characteristic. It is difficult to check, using numerical solutions of the hydrodynamic equations, whether the flow indeed approaches a delta=0 SLS behavior as R->∞, due to the slow convergence to SLS for omega~3. We show that in this case the flow may be described by a modified SLS solution, ḋ/dln R=delta with slowly varying delta(R), eta≡ d delta/dln R<<1, and spatial profiles given by a sum of the SLS solution corresponding to the instantaneous value of delta and a SLS correction linear in eta. The modified SLS solutions provide an excellent approximation to numerical solutions obtained for omega~3 at large R, with delta->0 (and eta≠0) for 3≤ omega≤ omegag. (abridged)
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A 2010 study studied this question.