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We are concerned with rigorous mathematical analysis of shock diffraction bytwo-dimensional convex cornered wedges in compressible fluid flow governed bythe nonlinear wave system. This shock diffraction problem can be formulated asa boundary value problem for second-order nonlinear partial differentialequations of mixed elliptic-hyperbolic type in an unbounded domain. It can befurther reformulated as a free boundary problem for nonlinear degenerateelliptic equations of second order. We establish a first global theory ofexistence and regularity for this shock diffraction problem. In particular, weestablish that the optimal regularity for the solution is $C^{0,1}$ across thedegenerate sonic boundary. To achieve this, we develop several mathematicalideas and techniques, which are also useful for other related problemsinvolving similar analytical difficulties.

Shock Diffraction by Convex Cornered Wedges for the Nonlinear Wave System