Shock Reflection in Plane Symmetry

We consider the problem of shock reflection on a solid wall in plane symmetry for a barotropic fluid. We establish a local-in-time solution after the point of reflection, thereby determining the state behind the reflected shock. The location of the reflected shock in space time being unknown the problem constitutes a free boundary problem. Furthermore, the quantity describing the thermodynamic state of the fluid along the wall being also unknown, complete data for the problem is only given in a single point, the reflection point.