  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. Experimental,
computational, and asymptotic analysis has shown that various patterns of shock
reflection may occur, including regular and Mach reflection. However, most of
the fundamental issues for shock reflection have not been understood, including
the global structure, stability, and transition of the different patterns of
shock reflection. Therefore, it is essential to establish the global existence
and structural stability of solutions of shock reflection in order to
understand fully the phenomena of shock reflection. On the other hand, there
has been no rigorous mathematical result on the global existence and structural
stability of shock reflection, including the case of potential flow which is
widely used in aerodynamics. Such problems involve several challenging
difficulties in the analysis of nonlinear partial differential equations such
as mixed equations of elliptic-hyperbolic type, free boundary problems, and
corner singularity where an elliptic degenerate curve meets a free boundary. In
this paper we develop a rigorous mathematical approach to overcome these
difficulties involved and establish a global theory of existence and stability
for shock reflection by large-angle wedges for potential flow. The techniques
and ideas developed here will be useful for other nonlinear problems involving
similar difficulties.
