Propagation of converging and diverging shock waves under isothermal condition

Abstract.

In this article the flows of perfect gas behind converging and diverging strong shock waves under isothermal condition in the cases of spherical and cylindrical symmetry are examined. A diverging shock wave is formed by energy supply according to a power law. These waves propagate in a uniform medium at rest and all conservation laws hold at the fronts of these shock waves. It was established that in the case of converging waves for any value of the ratios of specific heats $\gamma \in (1,3)$ the solution of the problem under consideration exists and is unique. When $\gamma \ge 3$ the problem has more than one solution. In the case of diverging shock waves the solution exists and is unique for any $\gamma$ from the interval $\gamma \in (1, 5/3]$ and any value of power in the energy input law.