Spherical steepened wave in interstellar van der Waals dusty gas clouds

This manuscript investigates one-dimensional steepened wave in self-gravitating, inviscid, and spherically symmetric flow of interstellar van der Waals dusty gas clouds via Guderley's exact similarity solution. The compatibility conditions are used to derive the transport equation for the jump in the velocity gradient. The effects of van der Waals excluded volume, mass fraction of solid particles in the mixture, ratio of specific heat of dust particles and specific heat of the interstellar van der Waals gas clouds at constant pressure, and the ratio of the species density of the solid particles to the species density of the gas on the steepened wave are determined in detail.