Shock wave kinematics in interstellar gas clouds with dust particles

In this article, a system of partial differential equations governing the one-dimensional motion of an inviscid gas with solid dust particles is considered. The evolutionary behavior of cylindrical and spherical shock waves in dusty gas is determined. To accomplish this, we used a technique that is based on the kinematics of the one-dimensional motion of shock waves. This allowed us to derive an infinite hierarchy of transport equations that describe the strength of shock waves and the induced discontinuity behind them. These equations are used to determine both the decay and growth behaviors of shock waves in dusty gas. Considering the first two truncation approximations, the results so obtained are compared with the results obtained by Guderley's exact solution and CCW approximation.