@inproceedings{b418514fc217456aaf3eab607216b7aa, title = "Existence and stability of global solutions of shock diffraction by wedges for potential flow", abstract = "We present our recent results on the mathematical analysis of shock diffraction by two-dimensional convex cornered wedges in compressible fluid flow governed by the potential flow equation. The shock diffraction problem can be formulated as an initial-boundary value problem, which is invariant under self-similar scaling. Then, by employing its self-similar invariance, the problem is reduced to a boundary value problem for a first-order nonlinear system of partial differential equations of mixed elliptic-hyperbolic type in an unbounded domain. It is further reformulated as a free boundary problem for a nonlinear degenerate elliptic system of first-order in a bounded domain with a boundary corner whose angle is bigger than π. A first global theory of existence and regularity has been established for this shock diffraction problem for the potential flow equation. {\textcopyright} Springer-Verlag Berlin Heidelberg 2014.", keywords = "Compressible flow, Free boundary, Mixed elliptic-hyperbolic type, Potential flow equation, Shock diffraction", author = "Chen, {Gui-Qiang G.} and Wei Xiang", year = "2014", doi = "10.1007/978-3-642-39007-4_6", language = "English", isbn = "9783642390067", volume = "49", pages = "113--142", booktitle = "Springer Proceedings in Mathematics and Statistics", note = "Workshop on Hyperbolic Conservation Laws and Related Analysis with Applications ; Conference date: 19-09-2011 Through 23-09-2011", }