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Shock Diffraction by Convex Cornered Wedges for the Nonlinear Wave System
We are concerned with rigorous mathematical analysis of shock diffraction by
two-dimensional convex cornered wedges in compressible fluid flow governed by
the nonlinear wave system. This shock diffraction problem can be formulated as
a boundary value problem for second-order nonlinear partial differential
equations of mixed elliptic-hyperbolic type in an unbounded domain. It can be
further reformulated as a free boundary problem for nonlinear degenerate
elliptic equations of second order. We establish a first global theory of
existence and regularity for this shock diffraction problem. In particular, we
establish that the optimal regularity for the solution is across the
degenerate sonic boundary. To achieve this, we develop several mathematical
ideas and techniques, which are also useful for other related problems
involving similar analytical difficulties.Comment: 50 pages;7 figure
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