Analytical Solutions for the Point Source Spherical Blast Wave Propagation with γ = 7

We consider the existence of a solution for the point-source spherical blast wave propagation caused by instantaneous explosion in case the ratio γ of the specific heats of the gas is 7. No similarity solutions of the Euler equations satisfy the conservation law on the shock front, so far as the atmospheric pressure ahead of the shock is not negligible. To describe the initial state, it can be used that the total amount of energy carried by the blast wave is constant and we use the condition of zero gas velocity at the center. By a hodograph transform this free boundary problem is converted into an eigenvalue. The problem for a system defined on a bounded rectangle such that this initial state assumption is satisfied. The solution is prescribed in the form of a power series expansion in one of the variables y = c 2 /u2 for front shock speed u and sound velocity c. Its convergence is shown by applying the fixed point theory of contractive mapping defined through linearization of the system. Our solution is local in y and exact there.