Evolution of steepened wave in interstellar gas clouds

The present paper focuses on studying the system of partial differential equations (PDEs) that describe the one-dimensional, spherically symmetric flow in an inviscid, self-gravitating, interstellar ideal gas cloud. The study aims to investigate the evolution of steepened waves, also known as discontinuity waves, within this system The Lie group of transformation, which leaves the system of partial differential equation invariant, is used to determine the particular exact solution to the governing system of PDEs. The propagation of a one-dimensional steepened wave in a spherically symmetric flow of gas is characterized by a particular exact solution. The evolution equation that governs the amplitude of a steepened wave can be derived using the singular surface theory and compatibility conditions. The obtained transport equation is integrated numerically and the effects of the exponent of the heating-cooling function, ambient density exponent, and specific heat ratio are observed on the steepened wave graphically.