  We investigate the interaction of two oncoming shock waves in spherical
symmetry for an ideal barotropic fluid. Our research problem is how to
establish a local in time solution after the interaction point and determine
the state behind the shock waves. This problem is a double free boundary
problem, as the position of the shock waves in space time is unknown. Our work
is based on a number of previous studies, including Lisibach's, who studied the
case of plane symmetry. To solve this problem, we will use an iterative regime
to establish a local in time solution.
