Concerning isothermal self-similar blast waves

The one-dimensional self-similar flow behind a blast wave from a plane explosion in a medium whose density varies with distance as xsup(-ω) is investigated with the assumption that the flow is isothermal. If ω < 0 a continuous solution passing through the origin and the shock does not exist. If 1/3 > ω > 0 one critical point exists. To be physically acceptable the flow must by-pass this critical point. It is shown that a continuous solution passing through both the origin and through the shock and by-passing the critical point does exist. If 1 > ω > 1/3 the first critical point does not exist but a second one appears. To be physically acceptable the flow must again by-pass this new critical point. It is shown that a continuous solution passing through both the origin and the shock and by-passing the new critical point exists in this case. If ω > 1 no physically acceptable solution exists since the mass behind the shock is infinite. (Auth.)