Gui-Qiang G. Chen, Xuemei Deng, Wei Xiang
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 $C^{0,1}$ 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.
View original:
http://arxiv.org/abs/1202.0856
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