  In this work we present a mathematical model for the propagation of the shock
waves that occur in graded density profiles. These waves can occur in a wide
range of astrophysical events, such as collisions in planetary and stellar
atmospheres, common envelope explosions and peculiar type Ia supernovae. The
behaviour of the shock wave and its evolution can be modelled using type II
self similar solutions. In such solutions the evolution of the shock wave is
determined by boundary conditions at the shock front and a singular point in
the shocked region. We show how the evolution can be determined for different
equations of state and density profiles, and compare these results to numerical
simulations. These findings are also applied to a variety of astrophysical
phenomena to further test their validity.
