Formation of standing shocks in stellar winds and related astrophysical flows

Stellar winds and other analogous astrophysical flows can be described, to lowest order, by the familiar one dimensional hydrodynamic equations which, being nonlinear, admit in some instances discontinuous as well as continuous transonic solutions for identical inner boundary conditions. The characteristics of the time dependent differential equations of motion are described to show how a perturbation changes profile in time and, under well defined conditions, develops into a stationary shock discontinuity. The formation of standing shocks in wind type astrophysical flows depends on the fulfillment of appropriate necessary conditions, which are determined by the conservation of mass, momentum and energy across the discontinuity, and certain sufficient conditions, which are determined by the flow's history.