If both winds are spherically symmetric and have constant mass-loss rates and velocities, the solution for the interacting winds is self-similar. The expansion of the circumstellar shell is dependent on the role of radiative cooling.

Both shocks are adiabatic: Expansion is given by semi-analytic self-similar solution (Chevalier & Imamura 1983).

Forward shock is radiative: Expansion velocity relative to the slow wind is given by (Chevalier 1988)

Both shocks are radiative: Expansion is found by balancing ram pressure