TY - GEN
T1 - Existence and stability of global solutions of shock diffraction by wedges for potential flow
AU - Chen, Gui-Qiang G.
AU - Xiang, Wei
PY - 2014
Y1 - 2014
N2 - 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. © Springer-Verlag Berlin Heidelberg 2014.
AB - 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. © Springer-Verlag Berlin Heidelberg 2014.
KW - Compressible flow
KW - Free boundary
KW - Mixed elliptic-hyperbolic type
KW - Potential flow equation
KW - Shock diffraction
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U2 - 10.1007/978-3-642-39007-4_6
DO - 10.1007/978-3-642-39007-4_6
M3 - 32_Refereed conference paper (with ISBN/ISSN)
SN - 9783642390067
VL - 49
SP - 113
EP - 142
BT - Springer Proceedings in Mathematics and Statistics
T2 - Workshop on Hyperbolic Conservation Laws and Related Analysis with Applications
Y2 - 19 September 2011 through 23 September 2011
ER -