Global Solutions of Shock Reflection by Wedges for the Nonlinear Wave Equation

When a plane shock hits a wedge head on, it experiences a reflection-diffraction process and then a self-similar reflected shock moves outward as the original shock moves forward in time. In this paper, shock reflection by large-angle wedges for compressible flow modeled by the nonlinear wave equation is studied and a global theory of existence, stability and regularity is established. Moreover, C ^0,1 is the optimal regularity for the solutions across the degenerate sonic boundary.